Chapter 2 - All 180 Problems!.xls

NOTES - CHAPTER 2 SOLUTIONS

FOLLOWING ARE SOME THOUGHTS ABOUT THE PROBLEMS AND SOLUTIONS IN THIS CHAPTER THAT MAY BE OF HELP TO FACULTY AND STUDENTS.

THIS IS, PERHAPS, THE MOST CRITICAL CHAPTER IN THE BOOK IN THAT IT DEALS WITH THE "TIME VALUE OF MONEY (TVM)," A FUNDAMENTAL CONCEPT USED THROUGHOUT THE REST OF THE BOOK.

THERE ARE 180 BASE PROBLEMS, MANY WITH MULTIPLE PARTS, AND MULTIPLE SOLUTIONS FOR MANY OF THOSE PARTS ARE PRESENTED IN THIS SOLUTION MANUAL

THERE ARE FIVE DIFFERENT METHODS THAT ARE SEEN MULTIPLE TIMES IN THESE SOLUTIONS. THEY INCLUDE USE OF (1) SIMPLE AND COMPOUND INTEREST FORMULAS, (2) INTEREST TABLES SUCH AS THOSE IN APPENDICES A AND B, AS WELL AS "ELECTRONIC" INTEREST TABLES (SEE ITEM 5 BELOW), (3) USE OF MYRIAD EXCEL FUNCTIONS, (4) SEARCH PROCEDURES USING EXCEL'S "SOLVER" AND "GOAL SEEK" TOOLS, AND (5) BRUTE FORCE TABULAR APPROACHES

THE COMPOUND INTEREST FORMULAS ARE OFTEN THE MOST ONEROUS TO USE, GIVEN THAT THEY REPRESENT THE FUNDAMENTAL MATHEMATICS OF TVM.

THE INTEREST TABLES REPRESENT THE MOST COMMON APPROACH USED HERETOFORE IN "ENGINEERING ECONOMY" COURSES; THEY USUALLY VASTLY SIMPLIFY THE MATHEMATICS INVOLVED BY INCORPORATING ONE OR MORE COMPOUND INTEREST FORMULAS INTO A SINGLE TABULATED "FACTOR" AVAILABLE IN APPENDICES A AND B. SINCE THE INTEREST TABLES ARE FOR ONLY A FINITE (ALTHOUGH VERY LARGE) SET OF INTEREST RATES (i AND j) AND TIME HORIZONS (n), THEY MAY NOT BE AVAILABLE FOR A SPECIFIC SET OF i, j, OR n NEEDED. "ELECTRONIC" INTEREST TABLES ARE AVAILABLE, AND HAVE BEEN USED WHEN UNAVAILABLE TABULATED VALUES OF i, j, AND/OR n HAVE BEEN NEEDED.

PROBLEMS 25, 63, 92, 123, AND 146 ASK FOR THE DEVELOPMENT OF CERTAIN INTEREST FACTORS SUCH AS ARE PRESENTED IN THE INTEREST TABLES. THESE SERVE TO CONVINCE THE STUDENT THAT THERE IS NO "MAGIC" INVOLVED IN THE INTEREST TABLES. IN ADDITION, THE FORMULAS USED IN DEVELOPING THE INTEREST FACTORS HAVE BEEN VERY USEFUL TO THE AUTHORS IN "COPY AND PASTE" OPERATIONS IN THE DEVELOPMENT OF THE CHAPTER 2 SOLUTIONS.

THE EXCEL FUNCTIONS HAVE NOT TRADITIONALLY BEEN WIDELY USED IN TEACHING "ENGINEERING ECONOMY." THEY HAVE, HOWEVER, BEEN USED IN THE WORLD OF FINANCE. THE EXCEL FUNCTIONS ARE WELL DESIGNED, AND PROVIDE A VERY PRECISE TOOL FOR USE IN SOLVING A WIDE ARRAY OF PROBLEMS INVOLVING TVM. BEWARE! FOR THE NOVICE, THESE EXCEL FUNCTIONS MAY APPEAR CONFUSING, COMPLEX, AND NOT WORTH THE TIME TO LEARN. THEY ARE, HOWEVER, QUITE STRAIGHTFORWARD AND CONSISTENT, ONCE ONE GETS PAST THE INITIAL TRIALS OF LEARNING SOMETHING NEW. THEY ARE LIKELY TO BE YOUR FAVORITE METHOD OF PROBLEM SOLUTION IF YOU USE THEM TO SOLVE OR CHECK YOUR SOLUTIONS IN THIS CHAPTER.

SOMETIMES, YOU WILL NEED TO SOLVE FOR A MONETARY VALUE, AN INTEREST RATE, A TIME INTERVAL, A GRADIENT, OR WHATEVER, NEEDED TO MATCH OTHER PARAMETERS OF A PROBLEM (E.G., WHAT INTEREST RATE MAKES AN INVESTMENT OF $100 WORTH $150 IN THREE YEARS). WHILE IT IS OFTEN POSSIBLE AND CONVENIENT TO USE ANALYTICAL APPROACHES (E.G., ALGEBRA), SOMETIMES THESE SOLUTIONS ARE DIFFICULT AND CUMBERSOME (ANALYTICALLY INTRACTABLE OR NEARLY SO). SEARCH PROCEDURES CAN BE VERY HANDY IN THESE CASES. EXCEL PROVIDES "SOLVER" AND "GOAL SEEK," BOTH OF WHICH RECEIVE SOME USE IN THE SOLUTIONS FOR CHAPTER 2. THE AUTHORS HAVE FOUND SOLVER TO BE QUITE ROBUST AND ACCURATE FOR THE PROBLEMS OF CHAPTER 2. GOAL SEEK, ALTHOUGH CLOSE, IS NOT QUITE AS CONSISTENT. BOTH ARE EASY TO USE.

THE "BRUTE FORCE" TABULAR APPROACH CAN BE VERY USEFUL WHEN A PROBLEM IS VERY COMPLEX AND DIFFICULT TO KEEP IN MIND WHILE ATTEMPTING TO USE AN INTEREST TABLE APPROACH OR AN EXCEL FUNCTION APPROACH. IN THESE INSTANCES, IT IS OFTEN USEFUL TO SIMPLY LIST THE ENTIRE SET OF CASH FLOWS, PERIOD BY PERIOD. THEN, OFTEN AN NPV FUNCTION OR AN FV-PLUS-NPV FUNCTION OR A PMT-PLUS-NPV FUNCTION CAN BE EASILY USED ON THE TABLE. THE BRUTE FORCE TABULAR APPROACH ALSO HAS THE ADVANTAGE THAT THE ENTIRE PATTERN OF CASH FLOWS CAN BE SEEN AND UNDERSTOOD. BE CAREFUL! ACTUALLY, MOST PROBLEMS CAN BE SOLVED USING THE BRUTE FORCE APPROACH - IN FACT, IT IS QUITE COMMONLY USED IN INDUSTRY! FOR NOW, WHILE LEARNING THIS MATERIAL, USE THE BRUTE FORCE APPROACH ONLY AS A LAST RESORT OR AS A PROBLEM CHECK AS HAS BEEN DONE IN THESE SOLUTIONS. TO USE THE BRUTE FORCE APPROACH ALONE IN CHAPTER 2 IS TO NOT LEARN THE OTHER APPROACHES.

IN THIS CHAPTER, WITH MULTIPLE APPROACHES USED IN SOLVING MANY PROBLEMS, THERE ARE OFTEN SLIGHTLY DIFFERENT SOLUTIONS ACHIEVED. THESE ARE NOT WRONG! USUALLY, IF NOT ALWAYS, THE INTEREST FORMULA APPROACH AND THE EXCEL FUNCTION APPROACH WILL BE PRECISELY THE SAME BECAUSE THERE IS VIRTUALLY NO ROUND OFF ERROR WITHIN THE COMPUTER. THE INTEREST TABLE APPROACH WILL BE SLIGHTLY DIFFERENT, DUE TO THE PRESENTATION OF INTEREST FACTORS TO FIVE PLACES AFTER THE DECIMAL IN MOST CASES. MANY TABLES USE ONLY FOUR PLACES. EVEN WITH FIVE PLACES, THERE WILL BE SOME MINOR DISCREPANCIES WHEN COMPARED TO THE EVEN MORE PRECISE APPROACHES. NOTE THAT SUCH DIFFERENCES ARE ALMOST ALWAYS INCONSEQUENTIAL BECAUSE THE ESTIMATES REQUIRED IN ECONOMIC EVALUATIONS ARE USUALLY ONLY APPROXIMATIONS ANYWAY.

EVEN THOUGH MANY PROBLEMS HAVE MULTIPLE PARTS, IT IS NOT INTENDED THAT ALL PARTS OF A PROBLEM NECESSARILY BE ASSIGNED AND WORKED. IN MANY CASES, THE LEARNING THAT TAKES PLACE CAN BE ACHIEVED BY WORKING ONLY ONE OR TWO PARTS. SEE, FOR EXAMPLE, PROBLEM 79.

WHILE MULTIPLE APPROACHES ARE OFTEN USED HEREIN TO SOLVE A PROBLEM, KEEP IN MIND THAT THERE ARE AN INFINITE (LITERALLY) NUMBER OF WAYS A TVM PROBLEM CAN BE SET UP AND SOLVED. TRANSLATION - THE SOLUTIONS PRESENTED HEREIN ARE QUITE DIRECT IN THEIR APPROACH, BUT NOT THE ONLY APPROACH.

PROBLEM 2.1

DCF STANDS FOR "DISCOUNTED CASH FLOW."

THE MOVEMENT OF MONEY FORWARD OR BACKWARD IN TIMEAN EXPLICIT METHOD FOR CONSIDERING THE TIME VALUE OF MONEY

A B123456

PROBLEM 2.2A

FOUR DCF RULES:

1. MONEY HAS A TIME VALUE

2. MONEY CANNOT BE ADDED OR SUBTRACTED UNLESS IT OCCURS AT THE SAME POINT(S) IN TIME

3. TO MOVE MONEY FORWARD ONE TIME UNIT, MULTIPLY TIMES ONE PLUS THE DISCOUNT OR INTEREST RATE

4. TO MOVE MONEY BACKWARD ONE TIME UNIT, DIVIDE BY ONE PLUS THE DISCOUNT OR INTEREST RATE

B12345

PROBLEM 2.3A

456789

THE WORTH OF THE DEAL RIGHT NOW IS $200 + $100/(1+0.05) = $295.24THE WORTH OF THE DEAL 1 YEAR FROM NOW IS $200*(1+0.05) + $100 = $310.00OR $295.24*(1+0.05) = $310.00

THE WORTH OF THE BUYER'S OFFER RIGHT NOW IS $300/(1+0.05) = $285.71THE WORTH OF THE BUYER'S OFFER 1 YEAR FROM NOW IS $300.00

THE OFFER IS NOT FAIR AND EQUITABLE BECAUSE THE BUYER IS VIOLATING THE DCF RULES. SPECIFICALLY, THE BUYER IS ADDING AND SUBTRACTING MONEY AT DIFFERENT POINTS IN TIME.

456789

PROBLEM 2.4

a FAIR AMOUNT NOW = $500 + $500/(1+0.06) = $971.70

b FAIR AMOUNT 1 YEAR FROM NOW = $500*(1+0.06) + $500 = $1030.00OR $971.70*(1+0.06) = $1030.00

A B123456

PROBLEM 2.5

CFD FROM BANK'S PERSPECTIVE

NOT NECESSARILY TO SCALE

(+) $X $X $X $X

0 1 2 3 4

$2,000

A B C D E F G123456789

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PROBLEM 2.6

CFD FROM YOUR PERSPECTIVE

$10,000

$4,000

0 1 2 3 4 5 6 7 8 9 10 11 12 13

(-)$2,880 $2,880 $2,880 $2,880 $2,880

$2,880 $2,880 $2,880 $2,880 $2,880

A B C D E F G H I J K L M N O123456789

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P123456789

10111213141516171819202122

PROBLEM 2.7

FROM KAELYN'S GRANDFATHER'S PERSPECTIVE$X+6000

NOT NECESSARILY TO SCALE $X+4500$X+3000

$X+1500(+) $X

$2,000

0 1 2 3 4 5 6 7 8 9 10 11

$30,000

A B C D E F G H I J K L M N123456789

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PROBLEM 2.8

CFD FROM DAVID'S PERSPECTIVE

$150,000

0 1 2 3 4 5 6 7 8

(-) $20,000 $20,000 $X

$X+8000$X+16,000

$X+24,000

A B C D E F G H I J123456789

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$X+24,000

K L123456789

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PROBLEM 2.9

CFD OF MERCRUISER CNC MACHINE

(+) $7,000 $7,000 $7,000 $7,000 $7,000 $7,000 $7,000 $7,000 $7,000 $7,000

0 1 2 3 4 5 6 7 8 9 10$1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000

(-) $1000+5000

SINCE PLANNING HORIZON IS 10 YEARS,WOULD NOT SHOW UPGRADE AT YEAR 10

$50,000

A B C D E F G H I J K L M123456789

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PROBLEM 2.10

CFD OF APARTMENT RENT

NOT NECESSARILY TO SCALE $450

0 1 2 3 4 5 6 7 8 9 10 11 12

(-) $150

$550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150

$550+450

A B C D E F G H I J K L M N123456789

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O123456789

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PROBLEM 2.11

USA DENIM (TWO MACHINES)

0 1 2 3 4 5 6 7

$12,000 $14,000

$16,000 $18,000

$20,000

$30,000

$38,000

$30,000+24,000

A B C D E F G H I123456789

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$22,000

J K123456789

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PROBLEM 2.12

LASER CUTTING MACHINE CFD

$14,000 $14,000 $14,000 $14,000 $14,000 $14,000

0 1 2 3 4 5 6$2,000

(-) $3,000 $4,000 $5,000

$23,000

A B C D E F G H I123456789

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PROBLEM 2.13

CFD OF SYNTHETIC RUBBER BLENDING MACHINE

NOT NECESSARILY TO SCALE$24,000-4000+8000-1600

$24,000-4000 $24,000-4000 $24,000-4000$18,000-1600 $24,000-4000 $24,000-4000 $24,000-4000

$12,000-1200$10,000-800

0 1 2 3 4 5 6 7 8 9 10

$62,000+8000

A B C D E F G H I J K L M123456789

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PROBLEM 2.14

i= 5.00%n= 12F= $8,000

a P= $5,000 USING SIMPLE INTEREST FORMULA THIS IS =8000/(1+0.05*12)

b P= $4,454.70 USING COMPOUND INTEREST FORMULA THIS IS =8000/(1+0.05)^12

P= $4,454.72 USING THE INTEREST TABLES THIS IS=$8,000*(P|F 5%,12)

P= $4,454.70 USING EXCEL'S PV FUNCTION THIS IS=PV(5%,12,,-8000)

A B C D E F G123456789

1011121314

PROBLEM 2.15

1 i= 5.50% SIMPLE INTERESTn= 5P= $10,000.00

F= $12,750.00 USING SIMPLE INTEREST FORMULA THIS IS =10000*(1+0.055*5)

2 i= 5.00% COMPOUNDED ANNUALLYn= 5P= $10,000.00

F= $12,762.82 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.05)^5

F= $12,762.80 USING THE INTEREST TABLES THIS IS $10,000*(F|P 5%,5)

F= $12,762.82 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,5,,-10000)

3 i= 6.50% SIMPLE INTERESTn= 5P= $10,000.00

4 i= 6.00% COMPOUNDED ANNUALLYn= 5P= $10,000.00

F= $13,382.26 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.06)^5

F= $13,382.30 USING THE INTEREST TABLES THIS IS= $10,000*(F|P 6%,5)

ACCOUNT 1 2 3 4AMOUNT $12,750.00 $12,762.82 $13,250.00 $13,382.26

ACCOUNT 4 IS PREFERRED SINCE IT GIVES THE HIGHEST FUTURE VALUE

A B C D E F G123456789

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PROBLEM 2.16

a i= 8.00% SIMPLE INTERESTn= 3P= $1,000.00

TOTAL INTEREST $240.00 THIS IS THE FUTURE VALUE OF $1,240 MINUSTHE PRESENT VALUE OF $1,000

b i= 8.00% COMPOUNDED ANNUALLYn= 3P= $1,000.00

F= $1,259.71 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.08)^3

F= $1,259.71 USING INTEREST TABLES THIS IS= $1,000*(F|P 8%,3)

TOTAL INTEREST $259.71 THIS IS THE FUTURE VALUE OF $1,259.71 MINUSTHE PRESENT VALUE OF $1,000.

A B C D E F G123456789

10111213141516171819202122232425

USING COMPOUND INTEREST FORMULAS THIS IS

H123456789

10111213141516171819202122232425

PROBLEM 2.17

a i= 12.00% SIMPLE INTERESTn= 5P= $3,000.00

F= $4,800.00 USING SIMPLE INTEREST FORMULA THIS IS =3000*(1+.012*5)

b i= 12.00% COMPOUNDED ANNUALLYn= 5P= $3,000.00

F= $5,287.02 USING INTEREST TABLES THIS IS=$3,000*(F|P 12%,5)

F= $5,287.03 USING EXCEL'S FV FUNCTION THIS IS=FV(12%,5,,-3000)

A B C D E F G H123456789

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PROBLEM 2.18

a i= 5.00%n= 3P= $1,000.00

b TOTAL INTEREST $150.00

c i= 5.00%n= 3P= $1,000.00

d TOTAL INTEREST $157.63 THIS IS THE FUTURE VALUE OF $1,157.63 MINUSTHE PRESENT VALUE OF $1,000.

A B C D E F G123456789

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H123456789

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PROBLEM 2.19

UNCLE ESWARi= 8.00% COMPOUNDED ANNUALLYn= 5P= $5,000.00

F= $7,346.65 USING INTEREST TABLES THIS IS =$5,000*(F|P 8%,5)

UNCLE SHANKARi= 9.00% SIMPLE INTERESTn= 5P= $5,000.00

GO WITH UNCLE SHANKAR'S LOAN

A B C D E F G123456789

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PROBLEM 2.20

a i= 8.00%n= 10F= $8,000.00

P= $3,705.55 USING COMPOUND INTEREST FORMULAS THIS IS =8000/(1+0.08)^10

P= $3,705.52 USING INTEREST TABLES THIS IS =$8,000*(P|F 8%,10)

b i= 11.59% USING SIMPLE INTEREST FORMULA THIS IS =(8000-3705.52)/(3705.52*10)

OR, CAN USE SOLVER TO FIND VALUE OF i

i= 11.59% <--SOLVER CHANGED CELLn= 10F= $8,000.00

P= $3,705.55 <--SOLVER TARGET CELLUSING SIMPLE INTEREST FORMULA THIS IS =8000/(1+i*10)

A B C D E F123456789

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PROBLEM 2.21

a i= 6.00%n= 4P= $12,000.00

b i= 6.56% USING SIMPLE INTEREST FORMULA THIS IS =(15149.72-12000)/(12000*4)

OR, CAN USE SOLVER TO FIND VALUE OF i

i= 6.56% <--SOLVER CHANGED CELLn= 4P= $12,000.00

F= $15,149.72 <--SOLVER TARGET CELLUSING SIMPLE INTEREST FORMULA THIS IS =12000*(1+i*4)

A B C D E F123456789

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PROBLEM 2.22

i= 7.00%n= 5P= $11,000.00

PRINCIPAL $11,000.00 FINAL AMT $15,428.07 INTEREST $4,428.07 =15428.07-11000.00

A B C D E F G H123456789

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PROBLEM 2.23

i= 8.00%n= 4P= $2,500.00

AT THE END OF 4 YEARS AT 8% SIMPLE INTEREST THE MAN HAS:F= $3,300.00 USING SIMPLE INTEREST FORMULA THIS IS

=2500*(1+0.08*4)

NOW, REINVESTING THE $3,300.00 FOR 9 YEARS RESULTS INi= 6.00%n= 9P= $3,300.00

AT THE END OF 9 MORE YEARS AT 6% COMPOUND INTEREST THE MAN HAS:F= $5,575.28 USING COMPOUND INTEREST FORMULAS THIS IS

=3300*(1+0.06)^9F= $5,575.28 USING INTEREST TABLES THIS IS

=$3,300*(F|P 6%,9)F= $5,575.28 USING EXCEL'S FV FUNCTION THIS IS

=FV(6%,9,,-3300)

A B C D E F G H I123456789

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PROBLEM 2.24

ACCOUNT1 i= 7.00%

n= 4P= $10,000.00

F= $13,108.00 USING INTER10,000*(F|P 7%,4)=$10,000*(F|P 7%,4)

2 i= 7.50%n= 4P= $10,000.00

3 i= 7.50%n= 4P= $10,000.00

F= $13,354.69 USING COMPOUND INTEREST FORMULAS THIS IS $13,354.69

F= $13,354.70 USING INTEREST TABLES (USER TAB) THIS IS =$10,000*(F|P 7.5%,4)

F= $13,354.69 USING EXCEL'S FV FUNCTION THIS IS=FV(7.5%,4,,-10000)

4 i= 8.25%n= 4P= $10,000.00

ACCOUNT 1 2 3AMOUNT OWED $13,107.96 $13,000.00 $13,354.69

PREFER LOAN 2

A B C D E F G123456789

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USING SIMPLE INTEREST FORMULA THIS IS

USING INTEREST TABLES (USER TAB) THIS IS

USING SIMPLE INTEREST FORMULA THIS IS

4$13,300.00

H123456789

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PROBLEM 2.25

i= 8.00%n= 3

(F|P i%,n) = 1.25971 USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.08)^3

i= 10.00%n= 20

(P|F i%,n) = 0.14864 USING COMPOUND INTEREST FORMULAS THIS IS =1/(1+0.1)^20

CHECKS OK WITH APPENDIX A

A B C D E F G H123456789

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PROBLEM 2.26

i= 8.00%n= 5P= $25,000.00

A B C D E F G H123456789

101112

PROBLEM 2.27

i= 4.00%n= 10F= $100,000.00

A B C D E F G123456789

101112

PROBLEM 2.28

i= 7.00%n= 10P= $25,000.00

F= $49,178.75 USING INTER25,000*(F|P 7%,10)=$25,000*(F|P 7%,10)

A B C D E F G123456789

101112

PROBLEM 2.29

i= 5.00%n= 25F= $150,000.00

A B C D E F G123456789

101112

PROBLEM 2.30

P= $0.04n= 49F= $0.41

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR ii=(F/P)^(1/n)-1

i= 4.8641% =(0.41/0.04)^(1/49)-1

OR, CAN USE RATE FUNCTIONP= $0.04n= 49F= $0.41

i= 4.8641% =RATE(49,,-0.04,0.41)

OR, CAN USE SOLVERP= $0.04 n= 49i= 4.8641% <--SOLVER CHANGED CELL

F= $0.41 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$0.04*(1+i)^49

F= $0.41 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,49,,-0.04)

A B C D E F G H123456789

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PROBLEM 2.31

a i= 8.00% COMPOUNDED ANNUALLYn= 10P= $1,000.00

F= $2,158.92 USING INTEREST TABLES THIS IS $1,000*(F|P 8%,10)

b i= 11.00%n= 4P= $5,000.00

c i= 9.00% COMPOUNDED ANNUALLYn= 7P= $13,000.00

d i= 10.00% COMPOUNDED ANNUALLYn= 3P= $25,000.00

A B C D E F G H123456789

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PROBLEM 2.32

a i= 5.00%n= 6F= $10,000.00

b i= 8.00%n= 4F= $6,500.00

c i= 6.00%n= 12F= $3,400.00

d i= 10.00%n= 5F= $13,500.00

A B C D E F G H123456789

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PROBLEM 2.33

a i= 14.00% COMPOUNDED ANNUALLYn= 7P= $3,000.00

F= $7,506.81 USING ELECTRONIC INTEREST TABLES THIS IS =$3,000*(F|P 14%,7)

b i= 12.00%n= 17P= $1,600.00

c i= 16.00% COMPOUNDED ANNUALLYn= 38P= $20,000.00

F= $5,629,030.30 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.16)^38

F= $5,629,030.20 USING ELECTRONIC INTEREST TABLES THIS IS =$20,000*(F|P 16%,38)

F= $5,629,030.30 USING EXCEL'S FV FUNCTION THIS IS =FV(16%,38,,-20000)

d i= 8.00% COMPOUNDED ANNUALLYn= 71P= $3,500.00

F= $826,332.22 USING ELECTRONIC INTEREST TABLES THIS IS =$3,500*(F|P 8%,71)

e i= 11.50% COMPOUNDED ANNUALLYn= 34P= $5,000.00

F= $202,448.95 USING ELECTRONIC INTEREST TABLES THIS IS =$5,000*(F|P 11.5%,34)

F= $202,448.93 USING EXCEL'S FV FUNCTION THIS IS

A B C D E F G H123456789

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=FV(11.5%,34,,-5000)A B C D E F G H

PROBLEM 2.34

a i= 9.00%n= 5F= $19,000.00

b i= 15.00%n= 12F= $8,300.00

c i= 12.00%n= 53F= $6,200.00

P= $15.27 USING COMPOUND INTEREST FORMULAS THIS IS =6200/(1+0.12)^53

P= $15.27 USING ELECTRONIC INTEREST TABLES THIS IS =$6,200*(P|F 12%,53)

P= $15.27 USING EXCEL'S PV FUNCTION THIS IS=PV(12%,53,,-6200)

d i= 19.20%n= 18F= $13,000.00

P= $550.77 USING COMPOUND INTEREST FORMULAS THIS IS =13000/(1+0.192)^18

P= $550.81 USING ELECTRONIC INTEREST TABLES THIS IS =$13,000*(P|F 19.2%,18)

P= $550.77 USING EXCEL'S PV FUNCTION THIS IS=PV(19.2%,18,,-13000)

e i= 8.00%n= 10F= $5,000.00

P= $2,315.97 USING EXCEL'S PV FUNCTION THIS IS

A B C D E F G H123456789

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=PV(8%,10,,-5000)A B C D E F G H

PROBLEM 2.35

a P= $10,000.00n= 10F= $23,674.00

i= 9.0002% =(23674/10000)^(1/10)-1

OR, CAN USE RATE FUNCTIONP= $10,000.00n= 10F= $23,674.00

i= 9.0002% =RATE(10,,-10000,23674)

OR, CAN USE SOLVERP= $10,000.00 n= 10

i= 9.0002% <--SOLVER CHANGED CELL

F= $23,674.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$10,000*(1+i)^10

F= $23,674.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,10,,-10000)

b P= $2,000.00n= 18F= $15,380.00

i= 12.0000% =(15380/2000)^(1/18)-1

i= 12.0000% =RATE(18,,-2000,15380)

OR, CAN USE SOLVER

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P= $2,000.00 n= 18

F= $15,380.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$2000*(1+i)^18

c P= $2,500.00n= 5F= $4,212.00

i= 10.9966% =(4212/2500)^(1/5)-1

i= 10.9966% =RATE(5,,-2500,4212)

F= $4,212.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$2500*(1+i)^5

F= $4,212.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,5,,2500)

A B C D E F G5657585960616263646566676869707172737475767778798081828384858687888990919293949596979899

PROBLEM 2.36

i= 11.00%n= 9F= $15,000.00

a P= $5,863.80 USING INTEREST TABLES THIS IS =$15,000*(P|F 11%,9)

b P= $5,863.87 USING COMPOUND INTEREST FORMULAS THIS IS =15000/(1+0.11)^9

c P= $5,863.87 USING EXCEL'S PV FUNCTION THIS IS=PV(11%,9,,-15000)

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PROBLEM 2.37

i= 8.00%

CHOICE 1: TAKE TODAYP= $1,000.00 ALREADY AT TIME 0

CHOICE 2: WAIT 3 YEARS AND TAKEF= $1,500.00 n= 3

CHOICE 3: WAIT 5 YEARS AND TAKEF= 3000n= 5

FOR EACH OF THE 3 CHOICES, DETERMINE THE VALUE AT THE SAME POINT IN TIME. BELOW, THE POINT IN TIME WILL BE THE PRESENT (TIME 0)

THE HIGHEST PRESENT VALUE IS ACHIEVED BY TAKING THE $3,000 AFTER 5 YEARS

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PROBLEM 2.38

i= 10.00%n= 7F= $23,384.61

TO FIND HOW MUCH HE BORROWED, FIND THE PW OF THE LOAN PAYOFF

P= $12,000.00 USING COMPOUND INTEREST FORMULAS THIS IS =23384.61/(1+0.1)^7

P= $12,000.05 USING INTEREST TABLES THIS IS =$23,384.61*(P|F 10%,7)

P= $12,000.00 USING EXCEL'S PV FUNCTION THIS IS=PV(10%,7,,-23384.61)

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PROBLEM 2.39

i= 11.50%n= 37SET THE FUTURE WORTH AT $1.00F= $1.00

THE (P|F 11.5%,37) FACTOR IS

P= 0.0178168 USING COMPOUND INTEREST FORMULAS THIS IS =1/(1+0.115)^37

P= 0.0178168 USING EXCEL'S PV FUNCTION THIS IS=PV(11.5%,37,,-1)

BOTH RESULTS ARE IDENTICAL

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PROBLEM 2.40

i= 12.00%n= 7F= $6,000.00

a P= $2,714.10 USING INTEREST TABLES THIS IS =$6,000*(P|F 12%,7)

b P= $2,714.10 USING COMPOUND INTEREST FORMULAS THIS IS =6000/(1+0.12)^7

c P= $2,714.10 USING EXCEL'S PV FUNCTION THIS IS=PV(12%,7,,-6000)

TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE WITHDRAWAL

A B C D E F G H123456

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TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE

I123456

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PROBLEM 2.41

P= $5,000.00n= 10F= $8,955.00

i= 6.0009% =(8955/5000)^(1/10)-1

i= 6.0009% =RATE(10,,-5000,8955)

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PROBLEM 2.42

P= $1,500.00n= 3F= $2,500.00

i= 18.5631% =(2500/1500)^(1/3)-1

i= 18.5631% =RATE(3,,-1500,2500)

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PROBLEM 2.43

P= $2,500.00i= 5.00%F= $4,430.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^nSOLVING FOR nn=ln(F/P)/ln(1+i)

n= 11.73 =LN(4430/2500)/LN(1+0.05)USE 12 YEARS

OR, CAN USE NPER EXCEL FUNCTIONP= $2,500.00i= 5.00%F= $4,430.00

n= 11.73 =NPER(5%,,-2500,4430)USE 12 YEARS

OR, CAN USE SOLVERP= $2,500.00 i= 5.00%

n= 11.73 <--SOLVER CHANGED CELLUSE 12 YEARS

F= $4,430.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$2,500*(1+0.05)^n

F= $4,430.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(5%,n,,-2500)

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PROBLEM 2.44

a P= $1.00n= 10F= $2.00

i= 7.1773% =(2/1)^(1/10)-1

i= 7.1773% =RATE(10,,-1.00,2.00)

b P= $1.00n= 10F= $3.00

i= 11.6123% =(3/1)^(1/10)-1

i= 11.6123% =RATE(10,,-1.00,3.00)

c P= $1.00n= 10F= $4.00

i= 14.8698% =(4/1)^(1/10)-1

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i= 14.8698% =RATE(10,,-1,4)

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PROBLEM 2.45

P= $1.00i= 9.00%F= $2.00

n= 8.04 =LN(2/1)/LN(1+0.09)USE 9 YEARS

OR, CAN USE NPER EXCEL FUNCTIONP= $1.00i= 9.00%F= $2.00

n= 8.04 =NPER(5%,,-2500,4430)USE 9 YEARS

OR, CAN USE SOLVERP= $1.00 i= 9.00%

F= $2.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$2,500*(1+0.05)^n

F= $2.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(5%,n,,-2500)

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PROBLEM 2.46

P= $1.00i= 6.00%F= $3.00

n= 18.85 =LN(3/1)/LN(1+0.06)USE 19 YEARS

n= 18.85 =NPER(6%,,-1.00,3.00)USE 19 YEARS

F= $3.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n

F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(6%,n,,-1.00)

A B C D E F123456789

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PROBLEM 2.47

P= $1.00n= 10F= $3.00

i= 11.6123% =(3/1)^(1/10)-1USE 12%

i= 11.6123% =RATE(10,,-1,3)USE 12%

OR, CAN USE SOLVERP= $1.00 n= 10

i= 11.6123% <--SOLVER CHANGED CELLUSE 12%

F= $3.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+i)^10

F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(i%,10,,-1)

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PROBLEM 2.48

a P= $1.00i= 6.00%F= $2.00

n= 11.90 =LN(2/1)/LN(1+0.06)USE 12 YEARS

n= 11.90 =NPER(6%,,-1.00,2.00)USE 12 YEARS

b P= $1.00i= 6.00%F= $3.00

n= 18.85 =LN(3/1)/LN(1+0.06)USE 19 YEARS

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n= 18.85 =NPER(6%,,-1.00,3.00)USE 19 YEARS

c P= $1.00i= 6.00%F= $4.00

n= 23.79 =LN(4/1)/LN(1+0.06)USE 24 YEARS

n= 23.79 =NPER(6%,,-1.00,4.00)USE 24 YEARS

F= $4.00 COULD HAVE USED THIS AS SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS

A B C D E5657585960616263646566676869707172737475767778798081828384858687888990919293949596979899

100101102103104105106107108109110

=FV(6%,n,,-1.00)A B C D E

PROBLEM 2.49

a i= 5.00%

APPR 1 APPR 2 APPR 314.40000 F|P 5%,14 1.97993 14.20670

=72/(100*0.05) F|P 5%,15 2.07893 =LOG(2)/LOG(1+0.05)INTERPOLATING 14.20273=14+(2-1.97993)/(2.07893-1.97993)

APPR 4 APPR 514.20670 n= 14.20670 <--SOLVER CHANGED CELL

=NPER(5%,,-1,2) F= $2.00 <--SOLVER TARGET CELL=FV(5%,n,,-1)

APPR 6n= 14.20658 <--GOAL SEEK CHANGED CELLF= $2.00 <--GOAL SEEK SET CELL

=FV(5%,n,,-1)

b i= 7.00%

APPR 1 APPR 2 APPR 310.28571 F|P 7%,10 1.96715 10.24477

=FV(5%,n,,-1)

c i= 10.00%

APPR 1 APPR 2 APPR 37.20000 F|P 10%,7 1.94872 7.27254

APPR 6n= 7.27432 <--GOAL SEEK CHANGED CELL

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F= $2.00 <--GOAL SEEK SET CELL=FV(5%,n,,-1)

d i= 15.00%

APPR 1 APPR 2 APPR 34.80000 F|P 15%,4 1.74901 4.95948

=FV(5%,n,,-1)

e i= 20.00%

APPR 1 APPR 2 APPR 33.60000 F|P 20%,3 1.72800 3.80178

=FV(5%,n,,-1)

A B C D E F G H56575859606162636465666768697071727374757677787980818283848586878889909192939495

PROBLEM 2.50

P= $176,000.00n= 9F= $525,000.00

i= 12.9116% =(525000/176000)^(1/9)-1

i= 12.9116% =RATE(9,,-176000,525000)

F= $525,000.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =$176000.00*(1+i)^9

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PROBLEM 2.51

i= 8.50%n= 10-4= 6P= $5,000.00

FINDING FW AT END OF YEAR 10 OF DEPOSIT AT END OF YEAR 4

F= $8,157.35 USING ELECTRONIC INTEREST TABLES THIS IS =$5,000*(F|P 8.5%,6)

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PROBLEM 2.52

i= 12.00%n= 40F= $15,000,000.00

P= $161,250.00 USING INTEREST TABLES THIS IS =$15,000,000*(P|F 12%,40)

TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE DESIRED FUTURE AMOUNT

A B C D E F G H123456

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PROBLEM 2.53

i= 7.50% COMPOUNDED ANNUALLYn= 10

EOY DEPOSIT0 $5,000.001 $1,000.002 $1,000.00

FIND THE FW OF EACH DEPOSIT AT YEAR 10F= $14,005.87 USING COMPOUND INTEREST FORMULAS THIS IS

=5000*(1+0.075)^10+1000*(1+0.075)^9+1000*(1+0.075)^8

FIND THE FW OF EACH DEPOSIT AT YEAR 10F= $14,005.87 USING ELECTRONIC INTEREST TABLES THIS IS

=$5,000*(F|P 7.5%,10)+$1,000*(F|P 7.5%,9)+$1,000*(F|P 7.5%,8)

FIND THE FW OF EACH DEPOSIT AT YEAR 10F= $14,005.87 USING EXCEL'S FV FUNCTION THIS IS

=FV(7.5%,10,,-5000)+FV(7.5%,9,,-1000)+FV(7.5%,8,,-1000)

SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FWF= $14,005.87 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS

=FV(7.5%,10,,-(NPV(7.5%,1000,1000)+5000))

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PROBLEM 2.54

EOY DEPOSIT0 $2,000.001 $0.002 $3,000.003 $0.004 $0.005 $4,000.006 $0.007 $1,000.00

FIND THE FW OF EACH DEPOSIT AT YEAR 15F= $19,949.14 USING COMPOUND INTEREST FORMULAS THIS IS

=2000*(1+0.06)^15+3000*(1+0.06)^13+4000*(1+0.06)^10+1000*(1+0.06)^8

FIND THE FW OF EACH DEPOSIT AT YEAR 15F= $19,949.16 USING INTEREST TABLES THIS IS

=$2,000*(F|P 6%,15)+$3,000*(F|P 6%,13)+$4,000*(F|P 6%,10)+$1,000*(F|P 6%,8)

FIND THE FW OF EACH DEPOSIT AT YEAR 15F= $19,949.14 USING EXCEL'S FV FUNCTION THIS IS

=FV(6%,15,,-2000)+FV(6%,13,,-3000)+FV(6%,10,,-4000)+FV(6%,8,,-1000)

SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FWF= $19,949.14 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS

=FV(6%,15,,-(NPV(6%,0,3000,0,0,4000,0,1000)+2000))

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=2000*(1+0.06)^15+3000*(1+0.06)^13+4000*(1+0.06)^10+1000*(1+0.06)^8

=$2,000*(F|P 6%,15)+$3,000*(F|P 6%,13)+$4,000*(F|P 6%,10)+$1,000*(F|P 6%,8)

=FV(6%,15,,-2000)+FV(6%,13,,-3000)+FV(6%,10,,-4000)+FV(6%,8,,-1000)

H I J123456789

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PROBLEM 2.55

EOY 0 1 2 3 4 5 6 7 8DEP/WDL $2,000.00 $0.00 $0.00 -$1,000.00 $0.00 $3,000.00 $0.00 $0.00 $1,500.00

FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11F= $8,831.27 USING COMPOUND INTEREST FORMULAS THIS IS

FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11F= $8,831.26 USING INTEREST TABLES THIS IS

FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11F= $8,831.27 USING EXCEL'S FV FUNCTION THIS IS

SUM THE PW OF EACH DEPOSIT OR WITHDRAWAL AND THEN FIND ITS FWF= $4,209.70 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS

=FV(7%,11,,-(NPV(7%,0,0,-1000,0,3000,0,0,1500)+2000))

=2000*(1+0.07)^11-1000*(1+0.07)^8+3000*(1+0.07)^6+1500*(1+0.07)^3

=$2,000*(F|P 7%,11)-$1,000*(F|P 7%,8)+$3,000*(F|P 7%,6)+$1,500*(F|P 7%,3)

=FV(7%,11,,-2000)+FV(7%,8,,1000)+FV(7%,6,,-3000)+FV(7%,3,,-1500)

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PROBLEM 2.56

i= 6.50%n= 7

EOY 0 1 2 3 4 5 6 7NCF $0.00 -$500.00 $200.00 $400.00 -$300.00 $500.00 -$200.00 $100.00

a F= $150.76 USING EXCEL'S FV FUNCTION THIS IS

$150.77 USING ELECTRONIC INTEREST TABLES THIS IS

b P= $97.02 USING EXCEL'S NPV FUNCTION THIS IS=NPV(6.5%,-500,200,400,-300,500,-200,100)+0

$97.02 USING ELECTRONIC INTEREST TABLES THIS IS

c P= $97.02 CONVERTING THE FW TO PW USING EXCEL'S PV FUNCTION=PV(6.5%,7,,-150.76)

$97.02 USING ELECTRONIC INTEREST TABLES THIS IS =$150.76*(P|F 6.5%,7)

=FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,-400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100

=-$500*(F|P 6.5%,6)+$200*(F|P 6.5%,5)+$400*(F|P 6.5%,4)-300*(F|P 6.5%,3)+500*(F|P 6.5%,2)-200*(F|P 6.5%,1)+100

=-$500*(P|F 6.5%,1)+$200*(P|F 6.5%,2)+$400*(P|F 6.5%,3)-$300*(P|F 6.5%,4)+$500*(P|F 6.5%,5)-$200*(P|F 6.5%,6)+$100*(P|F 6.5%,7)

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PROBLEM 2.57

i= 8.00%n= 6

EOY 0 1 2 3 4 5 6NCF $0.00 $500.00 -$200.00 $600.00 $300.00 -$100.00 $200.00

a P= $1,046.28 USING EXCEL'S NPV FUNCTION THIS IS=NPV(6.5%,-500,200,400,-300,500,-200,100)+0

$1,046.28 USING INTEREST TABLES THIS IS

b F= $1,660.31 USING EXCEL'S FV FUNCTION THIS IS

c P= $1,046.28 CONVERTING THE FW TO PW USING EXCEL'S PV FUNCTION=PV(8%,6,,-1660.31)

$1,046.28 USING INTEREST TABLES THIS IS =$1,660.31*(P|F 8%,6)

d FIND THE WORTH AT EOY 4F4= $1,423.45 USING EXCEL'S PV AND FV FUNCTIONS THIS IS

e CONVERT THE WORTH AT EOY 4 TO PRESENTP= $1,046.28 USING EXCEL'S PV FUNCTION THIS IS

=PV(8%,4,,-1423.45)$1,046.28 USING INTEREST TABLES THIS IS

=$1,423.45*(P|F 8%,4)

=$500*(P|F 8%,1)-$200*(P|F 8%,2)+$600*(P|F 8%,3)+$300*(P|F 8%,4)-$100*(P|F 8%,5)+$200*(P|F 8%,6)

=FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,-400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100

=$500*(F|P 8%,5)-$200*(F|P 8%,4)+$600*(F|P 8%,3)+$300*(F|P 8%,2)-$100*(F|P 8%,1)+$200

=FV(8%,3,,-500)+FV(8%,2,,200)+FV(8%,1,,-600)+300+PV(8%,1,,100)+PV(8%,2,,-200)

=$500*(F|P 8%,3)-200*(F|P 8%,2)+600*(F|P 8%,1)+$300-$100*(P|F 8%,1)+$200*(P|F 8%,2)

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PROBLEM 2.58

i= 6.00%

a $8,000

0 1 2 3 4 5 6 7 8

$X $X+100 $X+400

X= $2,272.61 <--SOLVER CHANGED CELL

P= $8,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV AND NPV FUNCTIONS THIS IS=PV(6%,4,,-NPV(6%,X,X+100,X+400,2*X))

CAN ALSO SOLVE USING INTEREST TABLES.

P= $8,000 USING INTEREST TABLES THIS IS =$X*(P|F 6%,5)+($X+$100)*(P|F 6%,6)+($X+$400)*(P|F 6%,7)+$2X*(P|F 6%,8)=$X*(0.74726)+($X+$100)*(0.70496)+($X+$400)*(0.66506)+$2X*(0.62741)=3.37210*X+$336.52

X= $2,272.61 =(8000-336.52)/3.3721

c EOY PAYMENT5 $2,272.61 $X6 $2,372.61 $X+1007 $2,672.61 $X+4008 $4,545.23 $2X

TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF RENALDO'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $8,000.

A B C D E F G H I J K123456789

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2122232425262728293031323334353637383940

=$X*(P|F 6%,5)+($X+$100)*(P|F 6%,6)+($X+$400)*(P|F 6%,7)+$2X*(P|F 6%,8)

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PROBLEM 2.59i= 5.50%

0 1 2 3 4 5 6 7 8

-$20,000.00

P= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV AND NPV FUNCTIONS THIS IS=PV(5.5%,3,,-NPV(5.5%,X,2*X,3*X,4*X,5*X))

CAN ALSO SOLVE USING INTEREST TABLES.

P= $20,000 USING ELECTRONIC INTEREST TABLES THIS IS

TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF REX'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $20,000.

=$X*(P|F 5.5%,4)+$2*X*(P|F 5.5%,5)+$3*X*(P|F 5.5%,6)+$4*X*(P|F 5.5%,7)+$5*X*(P|F 5.5%,8)

A B C D E F G H I J123456789

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41424344454647484950

=10.52099*XX= $1,900.96 =20000/10.52099

c EOY PAYMENT4 $1,900.97 5 $3,801.93 6 $5,702.90 7 $7,603.87 8 $9,504.83

d SUM $28,514.50 INTEREST $8,514.50 =28,514.50-20,000.00

AMOUNT OF KEN'S CHECK

=$X*(0.80722)+$2*X*(0.76513)+$3*X*(0.72525)+$4*X*(0.68744)+$5*X*(0.65160)

A B C D E F G H I J

53545556575859606162636465

TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF REX'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. THEN, USE

=$X*(P|F 5.5%,4)+$2*X*(P|F 5.5%,5)+$3*X*(P|F 5.5%,6)+

K123456789

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41424344454647484950

=$X*(0.80722)+$2*X*(0.76513)+$3*X*(0.72525)+$4*X*(0.68744)+

53545556575859606162636465

PROBLEM 2.60

i= 8.00%n= 8

EOY 0 1 2 3 4 5 6 7 8NCF $300.00 $300.00 $600.00 -$500.00 -$300.00 $0.00 $800.00 $700.00 $600.00

a P= $1,711.50 USING EXCEL'S NPV FUNCTION THIS IS=NPV(8%,300,600,-500,-300,0,800,700,600)+300

b F= $3,167.86 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,C4,,-C9)

F= $3,167.86 USING INTEREST TABLES THIS IS =$1,711.50*(F|P 8%,8)

c F2= $1,996.29 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,2,,-1711.5)

F2= $1,996.29 USING INTEREST TABLES THIS IS =$1,711.50*(F|P 8%,2)

=$300+$300*(P|F 8%,1)+$600*(P|F 8%,2)-$500*(P|F 8%,3)-$300*(P|F 8%,4)+$800*(P|F 8%,6)+$700*(P|F 8%,7)+$600*(P|F 8%,8)

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PROBLEM 2.61

i= 5.00%n= 8

EOY 0 1 2 3 4 5 6 7 8NCF $150.00 $300.00 $450.00 $0.00 -$500.00 $0.00 $600.00 $700.00 $800.00

a P= $1,919.20 USING COMPOUND INTEREST FORMULAS THIS IS

P= $1,919.21 USING INTEREST TABLES THIS IS

P= $1,919.20 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,300,450,0,-500,0,600,700,800)+150

b F= $2,835.54 USING COMPOUND INTEREST FORMULAS THIS IS

F= $2,835.54 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,8,,-1919.20)

c F6= $2,571.92 USING COMPOUND INTEREST FORMULAS THIS IS

F6= $2,571.93 USING INTEREST TABLES THIS IS =$1,919.20*(F|P 5%,6)

F6= $2,571.92 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,6,,-1919.20)

=150+300*(1+0.05)^-1+450*(1+0.05)^-2-500*(1+0.05)^-4+600*(1+0.05)^-6+700*(1+0.05)^-7+800*(1+0.05)^-8

=$150+$300*(P|F 5%,1)+$450*(P|F 5%,2)-$500*(P|F 5%,4)-$600*(P|F 5%,6)+$700*(P|F 5%,7)+$800*(P|F 5%,8)

=150*(1+0.05)^8+300*(1+0.05)^7+450*(1+0.05)^6-500*(1+0.05)^4+600*(1+0.05)^2+700*(1+0.05)^1+800

=150*(1+0.05)^6+300*(1+0.05)^5+450*(1+0.05)^4-500*(1+0.05)^2+600+700*(1+0.05)^-1+800*(1+0.05)^-2

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PROBLEM 2.62

i= 12.00%COST $30,000.00

PAYMENT METHOD 1GET CASH DISCOUNT= 3.00%

PW= $29,100.00 =30000*(1-0.03)

PAYMENT METHOD 2PAY ACCORDING TO THE FOLLOWING SCHEDULEEOY 0 1 2 3 4 5CF $5,000.00 $8,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00

PW= $28,414.37 USING EXCEL'S NPV FUNCTION THIS IS=NPV(12%,8000,6000,6000,6000,6000)+5000

PW= $28,414.40 USING INTEREST TABLES THIS IS

USE PAYMENT METHOD 2 - LOWER PW

=$5,000+$8,000*(P|F 12%,1)+$6,000*(P|F 12%,2)+$6,000*(P|F 12%,3)+$6,000*(P|F 12%,4)+$6,000*(P|F 12%,5)

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PROBLEM 2.63

P|A FACTOR

i= 8.00% USING 8% FOR EXAMPLE CALCn= 8 USING 8 FOR EXAMPLE CALC

(P|A i%,n)= 5.74664 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.08)^8-1)/(0.08*(1+0.08)^8)

A|P FACTOR

(A|P i%,n)= 0.21835 USING COMPOUND INTEREST FORMULAS THIS IS =(0.03*(1+0.03)^5)/((1+0.03)^5-1)

F|A FACTOR

(F|A i%,n)= 15.93742 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.1)^10-1)/0.1

A|F FACTOR

(A|F i%,n)= 0.18835 USING COMPOUND INTEREST FORMULAS THIS IS =0.03/((1+0.03)^5-1)

ALL CHECK OK WITH APPENDIX A

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PROBLEM 2.64

i= 9.00%n= 7P= $40,000.00

A= $7,947.62 USING COMPOUND INTEREST FORMULAS THIS IS =40000*(0.09*(1+0.09)^7)/((1+0.09)^7-1)

A= $7,947.60 USING INTEREST TABLES THIS IS 40,000*(A|P 9%,7)

A= $7,947.62 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.09,7,-40000)

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PROBLEM 2.65

i= 4.00%n= 10A= $5,000.00

F= $60,030.54 USING COMPOUND INTEREST FORMULAS THIS IS =5000*((1+0.04)^10-1)/0.04

F= $60,030.55 USING INTEREST TABLES THIS IS =$5,000*(F|A 4%,10)

F= $60,030.54 USING EXCEL'S FV FUNCTION THIS IS=FV(0.04,10,-5000)

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PROBLEM 2.66

i= 6.00%n= 8A= $7,500.00

P= $46,573.45 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.06)^8-1)/(0.06*(1+0.06)^8)

P= $46,573.43 USING INTEREST TABLES THIS IS =$7,500*(P|A 6%,8)

P= $46,573.45 USING EXCEL'S PV FUNCTION THIS IS=PV(6%,8,-7500)

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PROBLEM 2.67

i= 7.00%n= 35F= $2,000,000.00

A= $14,467.92 USING COMPOUND INTEREST FORMULAS THIS IS =2000000*0.07/((1+0.07)^35-1)

A= $14,468.00 USING ELECTRONIC INTEREST TABLES THIS IS =$2,000,000*(A|F 7%,35)

A= $14,467.92 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.07,35,,-2000000)

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PROBLEM 2.68

i= 7.00%n= 5P= $25,000.00

A= $6,097.27 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(0.07*(1+0.07)^5)/((1+0.07)^5-1)

A= $6,097.25 USING INTEREST TABLES THIS IS =$25,000*(A|P 7%,5)

A= $6,097.27 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.07,5,-25000)

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PROBLEM 2.69

a i= 4.00%n= 20A= $7,500.00

i= 4.00%n= 25A= $7,500.00

i= 4.00%n= 30A= $7,500.00

b i= 5.00%n= 20A= $7,500.00

i= 5.00%n= 25

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A= $7,500.00

i= 5.00%n= 30A= $7,500.00

c PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 4%=39.85% =(312344.31-223335.59)/223335.59

PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 4%=88.34% =(420637.03-223335.59)/223335.59

PERCENTAGE INCREASE FROM 4% TO 5% FOR 20 YEARS=11.04% =(247994.66-223335.59)/223335.59

AT 4%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 39.85% AND 88.34%, RESPECTIVELYAT 5%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 44.34% AND 100.93%, RESPECTIVELYA 25% INCREASE IN INTEREST RATE YIELDED INCREASED ACCUMULATIONS OF 11.04%, 14.60%, AND 18.46%, RESPECTIVELY, FOR 20, 25, AND 30 YEARS

A B C D E F G H535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697

AT 4%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 39.85% AND 88.34%, RESPECTIVELYAT 5%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 44.34% AND 100.93%, RESPECTIVELYA 25% INCREASE IN INTEREST RATE YIELDED INCREASED ACCUMULATIONS OF 11.04%, 14.60%, AND 18.46%, RESPECTIVELY, FOR 20, 25, AND 30 YEARS

I J K L M N O535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697

PROBLEM 2.70

a i= 7.00%n= 5P= $50,000.00

WITH THE FIRST PAYMENT AT THE END OF YEAR 1A= $12,194.53 USING COMPOUND INTEREST FORMULAS THIS IS

=50000*(0.07*(1+0.07)^5)/((1+0.07)^5-1)A= $12,194.50 USING INTEREST TABLES THIS IS

=$50,000*(A|P 7%,5)A= $12,194.53 USING EXCEL'S PMT FUNCTION THIS IS

=PMT(0.07,5,-50000)

b i= 7.00%n= 5 PAYMENTSt= 4 WITH FIRST PAYMENT AT EOY 4P= $50,000.00

WITH THE FIRST PAYMENT AT THE END OF YEAR 4FIND VALUE OF $50,000 AT EOY 3, THEN FIND AMOUNT OF 5 ANNUAL PAYMENTS

A= $14,938.83 USING COMPOUND INTEREST FORMULAS THIS IS =50000*((1+0.07)^(4-1))*(0.07*(1+0.07)^5)/((1+0.07)^5-1)

A= $14,938.75 USING INTEREST TABLES THIS IS =$50,000*(F|P 7%,3)*(A|P 7%,5)

A= $14,938.83 USING EXCEL'S PMT AND FV FUNCTIONS THIS IS=PMT(7%,5,-FV(7%,4-1,,-50000))

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PROBLEM 2.71

a i= 5.00%n= 10A= $5,000.00

WITH THE FIRST WITHDRAWAL AT THE END OF YEAR 1P= $38,608.67 USING COMPOUND INTEREST FORMULAS THIS IS

=5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)P= $38,608.65 USING INTEREST TABLES THIS IS

=$5,000*(P|A 5%,10)P= $38,608.67 USING EXCEL'S PV FUNCTION THIS IS

=PV(5%,10,-5000)

b i= 5.00%n= 10 WITHDRAWALSt= 3 WITH FIRST WITHDRAWAL AT EOY 3A= $5,000.00

WITH THE FIRST PAYMENT AT THE END OF YEAR 3FIND VALUE OF 10 ANNUAL WITHDRAWALS AT EOY 2, THEN FIND PRESENT WORTH

P= $35,019.21 USING COMPOUND INTEREST FORMULAS THIS IS =5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)*(1/(1+0.05)^(3-1))

P= $35,019.20 USING INTEREST TABLES THIS IS $5,000*(P|F 5%,2)*(P|A 5%,10)

P= $35,019.21 USING EXCEL'S PV FUNCTION THIS IS=PV(5%,3-1,,-PV(5%,10,-5000))

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FIND VALUE OF 10 ANNUAL WITHDRAWALS AT EOY 2, THEN FIND PRESENT WORTH

USING COMPOUND INTEREST FORMULAS THIS IS =5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)*(1/(1+0.05)^(3-1))

F123456789

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PROBLEM 2.72

LET'S CONSIDER INTEREST RATES FROM 0% TO 20%A= $10,000.00 $5,000.00 n= 5 10

PV OF PV OFINTEREST 10K FOR 5 YR 5K FOR 10 YR

0.00% $50,000.00 =PV(0%,5,-10000) $50,000.00 =PV(0%,10,-5000)1.00% $48,534.31 $47,356.52 2.00% $47,134.60 $44,912.93 3.00% $45,797.07 =PV(3%,5,-10000) $42,651.01 =PV(3%,10,-5000)4.00% $44,518.22 $40,554.48 5.00% $43,294.77 $38,608.67 6.00% $42,123.64 $36,800.44 7.00% $41,001.97 $35,117.91 8.00% $39,927.10 $33,550.41 9.00% $38,896.51 $32,088.29

10.00% $37,907.87 $30,722.84 11.00% $36,958.97 $29,446.16 12.00% $36,047.76 $28,251.12 13.00% $35,172.31 $27,131.22 14.00% $34,330.81 $26,080.58 15.00% $33,521.55 $25,093.84 16.00% $32,742.94 $24,166.14 17.00% $31,993.46 $23,293.02 18.00% $31,271.71 $22,470.43 19.00% $30,576.35 $21,694.67 20.00% $29,906.12 =PV(20%,5,-10000) $20,962.36 =PV(20%,10,-5000)

PREFER TO RECEIVE YOUR MONEY QUICKER AT $10K FOR EACH OF 5 YEARS

PREFER TO PAY YOUR MONEY OVER A LONGER PERIOD AT $5K FOR EACH OF 10 YEARS

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PREFER TO PAY YOUR MONEY OVER A LONGER PERIOD AT $5K FOR EACH OF 10 YEARS

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PROBLEM 2.73

a i= 6.00%n= 8

A(3 TO 10)= $10,000.00DISPLACED n= 2

A(1 TO 8)= $8,899.96 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.06)^2

A(1 TO 8)= $8,900.00 USING INTEREST TABLES THIS IS =$10,000*(P|F 6%,2)

A(1 TO 8)= $8,899.96 USING EXCEL'S PV FUNCTION THIS IS=PV(6%,2,,-10000)

A(1 TO 8)= $8,900.22 USING INTEREST TABLES THIS IS =$10,000*(P|A 6%,8)*(P|F 6%,2)*(A|P 6%,8)

A(1 TO 8)= $8,899.96 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS=PMT(6%,8,-PV(6%,2,,-PV(6%,8,-10000)))

b i= 10.00%n= 8

A(3 TO 10)= $10,000.00DISPLACED n= 2

A(1 TO 8)= $8,264.46 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.10)^2

A(1 TO 8)= $8,264.50 USING INTEREST TABLES THIS IS =$10,000*(P|F 10%,2)

A(1 TO 8)= $8,264.46 USING EXCEL'S PV FUNCTION THIS IS=PV(10%,2,,-10000)

A(1 TO 8)= $8,264.46 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS=PMT(10%,8,-PV(10%,2,,-PV(10%,8,-10000)))

A(1 TO 8)= $8,264.33 USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,8)*(P|F 10%,2)*(A|P 10%,8)

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 TWO YEARS EARLIER

OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 1-8.

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 TWO YEARS EARLIER

OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 1-8.

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PROBLEM 2.74

a i= 6.00%n= 10

A(3 TO 10)= $10,000.00DISPLACED n= 10

A(11 TO 20)= $17,908.48 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.06)^2

A(11 TO 20)= $17,908.50 USING INTEREST TABLES THIS IS =$10,000*(F|P 6%,10)

A(11 TO 20)= $17,908.48 USING EXCEL'S FV FUNCTION THIS IS=FV(6%,10,,-10000)

A(11 TO 20)= $17,908.74 USING INTEREST TABLES THIS IS =$10,000*(F|A 6%,10)*(A|P 6%,10)

A(11 TO 20)= $17,908.48 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS=PMT(6%,10,-FV(6%,10,,-PV(6%,10,-10000)))

b i= 10.00%n= 10

A(3 TO 10)= $10,000.00DISPLACED n= 10

A(11 TO 20)= $25,937.42 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.10)^2

A(11 TO 20)= $25,937.40 USING INTEREST TABLES THIS IS =$10,000*(F|P 10%,10)

A(11 TO 20)= $25,937.42 USING EXCEL'S FV FUNCTION THIS IS=FV(10%,10,,-10000)

A(11 TO 20)= $25,938.15 USING INTEREST TABLES THIS IS =$10,000*(F|A 10%,10)*(A|P 10%,10)

A(11 TO 20)= $25,937.42 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS=PMT(10%,10,-FV(10%,10,,-PV(10%,10,-10000)))

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 10 YEARS LATER

OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 11-20.

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 10 YEARS LATER

OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10 AT EOY 10, AND THEN USE THAT AMOUNT AS A PW TO DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES OVER YEARS 11-20.

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PROBLEM 2.75

i= 5.00%n= 10A= $1,000.00

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PROBLEM 2.76

a i= 8.00%n= 8A= $1,000.00

FINDING THE PW AT EOY 0P= $5,746.64 USING COMPOUND INTEREST FORMULAS THIS IS

=1000*((1+0.08)^8-1)/(0.08*(1+0.08)^8)P= $5,746.64 USING INTEREST TABLES THIS IS

=$1,000*(P|A 8%,8)P= $5,746.64 USING EXCEL'S PV FUNCTION THIS IS

=PV(8%,8,-1000)

b i= 8.00%n= 8A= $1,000.00

FINDING THE FW AT EOY 8F= $10,636.63 USING COMPOUND INTEREST FORMULAS THIS IS

=1000*((1+0.08)^8-1)/0.08F= $10,636.63 USING INTEREST TABLES THIS IS

=$1,000*(F|A 8%,8)F= $10,636.63 USING EXCEL'S FV FUNCTION THIS IS

=FV(0.08,8,-1000)

c i= 8.00%n= 8A= $1,000.00t= 11 THREE YEARS AFTER LAST DEPOSIT

FINDING THE FW AT EOY 11F= $13,399.09 USING COMPOUND INTEREST FORMULAS THIS IS

=1000*(((1+0.08)^8-1)/0.08)*(1+0.08)^3F= $13,399.07 USING INTEREST TABLES THIS IS

=$1,000*(F|A 8%,8)*F|P(8%,3)F= $13,399.09 USING EXCEL'S FV FUNCTION THIS IS

=FV(8%,11,,PV(8%,8,1000))

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PROBLEM 2.77

a A= $60,000.00 i= 10.00%

n(investment)= 19 1 YEAR BEFORE FIRST WITHDRAWALn(withdrawal)= 10 NUMBER OF WITHDRAWALS

P= $60,281.15 USING COMPOUND INTEREST FORMULAS THIS IS=60000*((1+0.1)^10-1)/(0.1*(1+0.1)^10)*(1+0.1)^-19

P= $60,281.92 USING INTEREST TABLES THIS IS $60,000*(P|A 10%,10)*(P|F 10%,19)

P= $60,281.15 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,20,,-PV(10%,10,-60000))

b A= $60,000.00 i= 15.00%

n(investment)= 19 1 YEAR BEFORE FIRST WITHDRAWALn(withdrawal)= 10 NUMBER OF WITHDRAWALS

P= $21,158.72 USING COMPOUND INTEREST FORMULAS THIS IS=60000*((1+0.15)^10-1)/(0.15*(1+0.15)^10)*(1+0.15)^-19

P= $21,160.14 USING INTEREST TABLES THIS IS $60,000*(P|A 15%,10)*(P|F 15%,19)

P= $21,158.72 USING EXCEL'S PV FUNCTION THIS IS =PV(15%,20,,-PV(15%,10,-60000))

FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND THE PW AT EOY 0.

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PROBLEM 2.78

i= 7.00%n= 12P= $200,000.00

WITH THE FIRST PAYMENT AT THE END OF YEAR 1A= $25,180.40 USING COMPOUND INTEREST FORMULAS THIS IS

=200000*(0.07*(1+0.07)^12)/((1+0.07)^12-1)A= $25,180.00 USING INTEREST TABLES THIS IS

=$200,000*(A|P 7%,12)A= $25,180.40 USING EXCEL'S PMT FUNCTION THIS IS

=PMT(0.07,12,-200000)

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PROBLEM 2.79

a A= $4,000.00 5.00%

F= $18,528.23 USING COMPOUND INTEREST FORMULAS THIS IS=4000*(((1+5%)^3-1)/5%)*(1+8%)^5

F= $18,528.25 USING INTEREST TABLES THIS IS =$4,000*(F|A 5%,3)*(F|P 8%,5)

F= $18,528.23 USING EXCEL'S FV FUNCTION THIS IS=FV(8%,5,,-FV(5%,3,-4000))

b A= $12,000.00 10.00%

c A= $18,000.00 9.00%

FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD.

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PROBLEM 2.80

a A= $2,000.00 i= 5.00%n= 15

F= $43,157.13 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,15,-2000)

b A= $3,000.00 i= 8.00%

n(deposits=) 10n(more years) 5

F= $63,856.54 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(((1+0.08)^10-1)/0.08)*(1+0.08)^5

ci= 8.00%

A(1st)= $2,000.00 n(1st)= 5A(2nd)= $4,000.00 n(2nd) 5A(3rd)= $6,000.00 n(3rd)= 5

F= $95,010.53 TABLES

F= $95,010.55 EXCEL

=$2,000*(F|A 8%,5)*(F|P 8%,10)+$4,000*(F|A 8%,5)*(F|P 8%,5)+$6,000*(F|A 8%,5)

=FV(8%,5,-6000)+FV(8%,5,,-FV(8%,5,-4000))+FV(8%,5+5,,-FV(8%,5,-2000))

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PROBLEM 2.81

i= 5.00%

$1,200.00 YEARS 1-5

5 DEPOSITS YEARS 1-5

-$700.00 YEARS 4-7

4 WITHDRAWALS YEARS 4-7

4 START TIME OF WITHDRAWALS

P= $3,051.18 USING INTEREST TABLES THIS IS =$1,200*(P|A 5%,5)-$700*(P|A 5%,4)*(P|F 5%,3)

P= $3,051.18 USING EXCEL'S FV FUNCTION THIS IS=PV(5%,5,-1200)-PV(5%,3,,-PV(5%,4,-700))

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PROBLEM 2.82

aP= $1.00 i= 7.000%A= $0.20 20% OF P

n= 6.367 USING EXCEL'S NPER FUNCTION THIS IS=NPER(7%,0.2,-1)

COULD ALSO USE SOLVER TO DETERMINE n

n= 6.367 <--SOLVER CHANGED CELL

P= $1.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=PV(7%,n,-0.2)

b P= $1.00 n= 7A= $0.20

i= 9.196% USING EXCEL'S RATE FUNCTION THIS IS=RATE(7,0.2,-1)

COULD ALSO USE SOLVER TO DETERMINE i

P= $1.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=PV(i%,7,-0.2)

SINCE THE AMOUNT PAID IS NOT GIVEN, ANY AMOUNT WILL SERVE TO ANSWER THE PROBLEM. A VALUE OF $1.00 IS SELECTED HERE

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PROBLEM 2.83

P= $6.00 n= 7A= $1.00

i= 4.009% USING EXCEL'S RATE FUNCTION THIS IS=RATE(7,0.2,-1)

COULD ALSO USE SOLVER TO DETERMINE i

P= $6.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=PV(i,7,-C6)

SINCE THE AMOUNT OF THE LOAN IS NOT GIVEN, ANY AMOUNT WILL SERVE TO ANSWER THE PROBLEM. A VALUE OF $6.00 IS SELECTED HERE.

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PROBLEM 2.84

i= 9.00%n1= 25 NUMBER OF DEPOSITSA= $4,000.00t= 28 TIME OF FIRST WITHDRAWAL

n2= 30 NUMBER OF WITHDRAWALS

F27= $402,532.54 USING COMPOUND INTEREST FORMULAS THIS IS =4000*(((1+0.09)^25-1)/0.09)*(1+0.09)^2

F27= $402,532.56 USING INTEREST TABLES THIS IS =$4,000*(F|A 9%,25)*(F|P 9%,2)

F27= $402,532.54 USING EXCEL'S FV FUNCTION THIS IS=FV(9%,28-25-1,,-FV(9%,25,-4000))

A= $39,181.05 USING COMPOUND INTEREST FORMULAS THIS IS =402532.54*(0.09*(1+0.09)^30)/((1+0.09)^30-1)

A= $39,182.52 USING INTEREST TABLES THIS IS =$402,532.54*(A|P 9%,30)

A= $39,181.05 USING EXCEL'S PMT FUNCTION THIS IS=PMT(9%,30,-402532.54)

c FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWN

A= $36,227.93 =402532.54*0.09

FIRST, DETERMINE THE AMOUNT IN THE ACCOUNT RIGHT AFTER THE LAST DEPOSIT AT EOY 25. THEN, FIND THE FW OF THAT AMOUNT ONE YEAR BEFORE THE FIRST WITHDRAWAL AT EOY 27

USING THE ANSWER TO PART a, FIND THE PAYMENT AMOUNT OVER THE WITHDRAWAL PERIOD

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PROBLEM 2.85

i= 12.00%n DEPOSITS= 30

A= $7,500.00 ($5,000 FROM YOU + $2,500 FROM EMPLOYER)n WITHDRAWALS= 30

a F= $1,809,995.13 USING COMPOUND INTEREST FORMULAS THIS IS =7500*(((1+0.12)^30-1)/0.12)

F= $1,809,995.10 USING INTEREST TABLES THIS IS =$7,500*(F|A 12%,30)

F= $1,809,995.13 USING EXCEL'S FV FUNCTION THIS IS=FV(12%,30,-7500)

b SUM(YOU)= $150,000.00 =5000*30

c SUM(EMPLOYER)= $75,000.00 =2500*30

d EARNINGS= $1,584,995.13 $1,584,995.13

A= $224,699.42 USING COMPOUND INTEREST FORMULAS THIS IS =1809995.13*(0.12*(1+0.12)^30)/((1+0.12)^30-1)

A= $224,692.80 USING INTEREST TABLES THIS IS =$1,809,995.13*(A|P 12%,30)

f FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWNINTEREST ONLY= $217,199.42 =1809995.13*0.12

USING THE ANSWER TO PART a, FIND THE YEARLY AMOUNT OVER THE WITHDRAWAL PERIOD

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PROBLEM 2.86

i= 6.00%P= $10,000.00 DEPOSIT AT EOY 0A= -$1,000.00 WITHDRAWALS AT EOY 3-7

10 YEARS FROM DEPOSIT TO FINAL WITHDRAWAL

5 YEARS OF WITHDRAWALS (3, 4, 5, 6, 7)

3 YEARS FROM 5TH WITHDRAWAL TO FINAL WITHDRAWAL

FIND THE FW AT EOY 10 OF THE INITIAL DEPOSIT AND THE FIVE WITHDRAWALS

F= $11,194.61 USING INTEREST TABLES THIS IS =$10,000*(F|P 6%,10)-$1,000*(F|A 6%,5)*(F|P 6%,3)

F= $11,194.61 USING EXCEL'S FV FUNCTION THIS IS=FV(6%,10,,-10000)+FV(6%,3,,-FV(6%,5,-(-1000)))

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PROBLEM 2.87

i= 12.00%

P= $15,000.00 LOAN VALUE AT EOY 0A= $3,000.00 PAYMENTS AT EOY 1, 2, 3, 4

4 YEARS UNTIL FINAL A=$3,000 PAYMENT

1 ADDITIONAL YEARS UNTIL FINAL PAYMENT

F= $10,376.58 USING COMPOUND INTEREST FORMULAS THIS IS =15000*(1+0.12)^(4+1)-(3000*(((1+0.12)^4-1)/0.12))*(1+0.12)^1

F= $10,376.55 USING INTEREST TABLES THIS IS =$15,000*(F|P 12%,5)-$3,000*(F|A 12%,4)*(F|P 12%,1)

F= $10,376.58 USING EXCEL'S FV FUNCTION THIS IS=FV(12%,4+1,,-15000)+FV(12%,1,,-FV(12%,4,3000))

F= $10,376.58 IS THE AMOUNT OF THE YEAR 5 PAYMENT

FIND THE LOAN VALUE AT EOY 5 AND SUBTRACT OFF THE PAYMENT VALUES AT EOY 5. WHAT'S LEFT IS THE FINAL LOAN PAYMENT AT EOY 5.

A B C D E F G H123456

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PROBLEM 2.88

i= 9.00%n1= 10 YEARS OF WITHDRAWALS

5 WITHDRAWALS REMAINING AT EOY 45AMT45= $32,801.60 AMOUNT LEFT IN ACCT AT EOY 45

THE FOLLOWING WILL BE NEEDED IN THE LAST STEPS OF THE PROBLEM

15 YEARS FROM DEPOSIT 1 TO EOY 40

FIRST, DETERMINE THE AMOUNT OF THE ANNUAL WITHDRAWALSA= $8,432.96 USING INTEREST TABLES THIS IS

=$32,801.60*(A|P 9%,5)A= $8,433.04 USING EXCEL'S PMT FUNCTION THIS IS

=PMT(9%,5,-32801.6)

AMT40= $54,120.41 USING INTEREST TABLES THIS IS =$8433.04*(P|A 9%,10)

AMT40= $54,120.39 USING EXCEL'S PV FUNCTION THIS IS=PV(9%,10,-8433.04)

AMT40= =7.54846 USING INTEREST TABLES THIS IS TIMES X =(F|P 9%,15)+(F|P 9%,10)+(F|P 9%,5)

=(3.64248+2.36736+1.53862)=7.54846

X= $7,169.73 =$54,120.41/7.54846

AMT40= 7.54847 USING EXCEL'S FV FUNCTION THIS ISTIMES X =(FV(9%,15,,-1)+(FV(9%,10,,-1)+(FV(9%,5,,-1))))

X= $7,169.72 =54120.39/7.54847******************************************************THIS PROBLEM MAY BETTER BE ANSWERED USING SOLVER

SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40AMT40= $54,120.44 USING INTEREST TABLES THIS IS

X*(F|P 9%,15)+X*(F|P 9%,10)+X*(F|P 9%,5)NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50

A= $8,433.05 =$54,120.84*(A|P 9%,10)=$54,120.84*0.15582

NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45AMT45= $32,801.60 <--SOLVER TARGET CELL

=$8,433.11*(P|A 9%,5)

NOW KNOWING THE ANNUAL WITHDRAWAL, DETERMINE THE AMOUNT IN THE ACCOUNT AT EOY 40

NOW, DETERMINE THE VALUE AT EOY 40 OF THE THREE "$X" DEPOSITS AT EOY 25, 30, AND 35 AND SOLVE FOR X

LET X BE ANY VALUE AT THIS POINT. SET UP ALL FOLLOWING EQUATIONS AS IF THE VALUE OF X IS RIGHT. SOLVER WILL LATER BE USED TO CORRECTLY SEARCH FOR AND SET THE VALUE OF X

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SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40AMT40= $54,120.39 USING EXCEL'S FV FUNCTION THIS IS

=(FV(9%,15,,-X)+FV(9%,10,,-X)+(FV(9%,5,,-X))NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50

NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45AMT45= $32,801.60 <--SOLVER TARGET CELL

USING EXCEL'S PV FUNCTION THIS IS=PV(9%,5,-8433.12)

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TIMES X

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PROBLEM 2.89

P= $20,000.00 AT EOY 30i= 5% YEARS 31-40i= 6% YEARS 41-50i= 7% YEARS 51 AND BEYOND

10 YEARS AT 5%

10 YEARS AT 6%

10 YEARS AT 7%

10 YEARS OF WITHDRAWALS

5 YEARS OF WITHDRAWALS REMAINING AT EOY 65

a FIRST, SOLVE FOR THE AMOUNT AVAILABLE AT EOY 60AMT60= $114,767.37 USING INTEREST TABLES THIS IS

=$20,000*(F|P 5%,10)*(F|P 6%,10)*(F|P 7%,10)A= $16,340.58 USING INTEREST TABLES THIS IS

=$114,767.37*(A|P 7%,10)AMT60= $114,767.63 USING EXCEL'S FV FUNCTION THIS IS

=FV(7%,10,,-FV(6%,10,,-FV(5%,10,,-20000)))A= $16,340.33 USING EXCEL'S PMT FUNCTION THIS IS

=PMT(7%,10,-114767.63)

WDL65= $83,340.22 USING INTEREST TABLES THIS IS =$16,340.58*(P|A 7%,5)+$16,340.58

WDL65= $83,338.90 USING EXCEL'S PV FUNCTION THIS IS=PV(7%,5,-16340.33)+16340.33

SOLVE FOR THE PW OF THE 5 REMAINING WITHDRAWALS AT EOY 66-70 PLUS THE WITHDRAWAL DUE AT EOY 65

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PROBLEM 2.90

i= 10.00%n= 8

EOY 0 1 2 3 4 5 6 7 8CF -$2,500.00 $3,000.00 $4,500.00 $0.00 -$5,000.00 $0.00 -$1,000.00 $7,000.00 $3,000.00

A= $929.41 USING INTEREST TABLES THIS IS =$4,958.43*(A|P 10%,8)

P= $4,958.37 USING EXCEL'S NPV FUNCTION THIS IS=NPV(10%,3000,4500,0,-5000,0,-1000,7000,3000)-2500

A= $929.42 USING EXCEL'S PMT FUNCTION THIS IS=PMT(C3,C4,-C10)

FIRST, FIND THE PW OF THIS CASH FLOW SERIES. THEN FIND THE EQUIVALENT VALUE OF "A"

=$2,500+$3,000*(P|F 10%,1)+$4,500*(P|F 10%,2)-$5,000*(P|F 10%,4)-$1,000*(P|F 10%,6)+$7,000*(P|F 10%,7)+$3,000*(P|F 10%,8)

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PROBLEM 2.91

a F= B*(F|P i%,1)*(F|A i%,n)

b F= B*(1+i)*((1+i)^n-1)/i

c B= $1,000.00n= 5i= 10.00%

USING (a) F= $6,715.61 USING INTEREST TABLES THIS IS =$1,000*(F|P 10%,1)*(F|P 10%,5)

USING (b) F= $6,715.61 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.1)*((1+0.1)^5-1)/0.1

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PROBLEM 2.92

P|G FACTOR

P|G= 2.44500 USING COMPOUND INTEREST FORMULAS THIS IS =(1-(1+3*0.08)*(1+0.08)^(-3))/(0.08^2)

F|G FACTOR NOT TABULATED IN APPENDIX A

F|G= 902.78225 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.12)^25-(1+25*0.12))/(0.12^2)

A|G FACTOR

A|G= 3.72546 USING COMPOUND INTEREST FORMULAS THIS IS =(1/0.10)-(10/0.10)*(0.10/((1+0.10)^10-1))

P|G AND A|G CHECK OK WITH APPENDIX A

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PROBLEM 2.93

i= 5.00%n= 5

$800.00 G= $100.00

P= $4,287.28 USING INTEREST TABLES THIS IS =$800*(P|A 5%,5)+$100*(P|G 5%,5)

P= $4,287.27 USING EXCEL'S NPV FUNCTION=NPV(5%,800,900,1000,1100,1200)

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER

EOY CF0 $0.00 1 $800.00 2 $900.00 3 $1,000.00 4 $1,100.00 5 $1,200.00

P= $4,287.27 =NPV(5%,800,900,1000,1100,1200)+0

A B C D E F G H1234

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PROBLEM 2.94

i= 6.00%n= 7

$5,000.00 G= $1,000.00

FV= $65,199.79 USING INTEREST TABLES THIS IS =($5,000*(P|A 6%,7)+$1,000*(P|G 6%,7))*F|P 6%,7

FV= $65,199.82 USING EXCEL'S FV AND NPV FUNCTIONS=FV(6%,7,,-NPV(6%,5000,6000,7000,8000,9000,10000,11000))

EOY CF0 $0.00 1 $5,000.00 2 $6,000.00 3 $7,000.00 4 $8,000.00 5 $9,000.00 6 $10,000.00 7 $11,000.00

FV= $65,199.82 =FV(6%,7,,-(NPV(6%,5000,6000,7000,8000,9000,10000,11000)+0))

A B C D E F G H1234

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=($5,000*(P|A 6%,7)+$1,000*(P|G 6%,7))*F|P 6%,7

=FV(6%,7,,-NPV(6%,5000,6000,7000,8000,9000,10000,11000))

=FV(6%,7,,-(NPV(6%,5000,6000,7000,8000,9000,10000,11000)+0))

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PROBLEM 2.95

i= 8.00%n= 6

$12,000.00G= -$2,000.00

P= $34,428.02 USING INTEREST TABLES THIS IS =$12,000*(P|A 8%,6)-$2,000*(P|G 8%,6)

P= $34,428.01 USING EXCEL'S NPV FUNCTION=NPV(8%,12000,10000,8000,6000,4000,2000)

EOY CF0 $0.00 1 $12,000.00 2 $10,000.00 3 $8,000.00 4 $6,000.00 5 $4,000.00 6 $2,000.00

P= $34,428.01 =NPV(8%,12000,10000,8000,6000,4000,2000)+0

A B C D E F G H1234

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PROBLEM 2.96

i= 10.00%n= 4

$2,000.00G= $500.00

a P= $8,528.80 USING INTEREST TABLES THIS IS =$2,000*(P|A 10%,4)+$500*(P|G 10%,4)

P= $8,528.79 USING EXCEL'S NPV FUNCTION=NPV(10%,2000,2500,3000,3500)

b A= $2,690.58 USING INTEREST TABLES THIS IS =$8,528.80*(A|P 10%,4)

A= $2,690.59 USING INTEREST TABLES THIS IS =$2,000+$500*(A|G 10%,4)

A= $2,690.58 USING EXCEL'S PMT FUNCTION=PMT(10%,4,-8528.79)

EOY CF0 $0.00 1 $2,000.00 2 $2,500.00 3 $3,000.00 4 $3,500.00

P= $8,528.79 =NPV(10%,2000,2500,3000,3500)+0

A= $2,690.58 =PMT(10%,4,-8528.79)

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PROBLEM 2.97

i= 12.00%n= 6

-$2,000.00G= $1,000.00

P= $707.35 USING INTEREST TABLES THIS IS -$2,000*(P|A 12%,6)+$1,000*(P|G 12%,6)

P= $707.36 USING EXCEL'S NPV FUNCTION THIS IS=NPV(12%,-2000,-1000,0,1000,2000,3000)

EOY CF0 $0.001 -$2,000.002 -$1,000.003 $0.004 $1,000.005 $2,000.006 $3,000.00

P= $707.36 =NPV(12%,-2000,-1000,0,1000,2000,3000)+0

A B C D E F G H I1234

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PROBLEM 2.98

a i= 6.00%n= 8

INITIAL CF= -$75,000.00

$3,000.00G= $3,000.00

P= $3,154.11 USING INTEREST TABLES THIS IS =-$75,000+3,000*(P|A 6%,8)+3,000*(P|G 6%,8)

P= $3,154.12 USING EXCEL'S NPV FUNCTION THIS IS

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWEREOY CF

0 -$75,000.001 $3,000.002 $6,000.003 $9,000.004 $12,000.005 $15,000.006 $18,000.007 $21,000.008 $24,000.00

P= $3,154.12

b i= 7.00%n= 8

INITIAL CF= -$75,000.00

$3,000.00G= $3,000.00

P= -$719.28 USING INTEREST TABLES THIS IS =-$75,000+3,000*(P|A 7%,8)+3,000*(P|G 7%,8)

P= -$719.29 USING EXCEL'S NPV FUNCTION THIS IS

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWEREOY CF

0 -$75,000.001 $3,000.002 $6,000.003 $9,000.004 $12,000.005 $15,000.006 $18,000.007 $21,000.008 $24,000.00

=NPV(6%,3000,3000+3000,3000+2*3000,3000+3*3000,3000+4*3000,3000+5*3000,3000+6*3000,3000+7*3000)-75000

=NPV(6%,3000,6000,9000,12000,15000,18000,21000,24000)-75000

=NPV(7%,3000,3000+3000,3000+2*3000,3000+3*3000,3000+4*3000,3000+5*3000,3000+6*3000,3000+7*3000)-75000

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P= -$719.29 =NPV(7%,3000,6000,9000,12000,15000,18000,21000,24000)-75000

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PROBLEM 2.99

a i= 5.00%n= 35

INITIAL CF= $0.00

$7,500.00G= $1,000.00

FW= $1,783,809.42 USING ELECTRONIC INTEREST TABLES THIS IS $0+$7,500*(F|A 5%,35)+$1,000*(P|G 5%,35)*(F|P 5%,35)

b i= 6.00%n= 35

INITIAL CF= $0.00

$7,500.00G= $1,000.00

FW= $2,109,674.39 USING ELECTRONIC INTEREST TABLES THIS IS $0+$7,500*(F|A 6%,35)+$1,000*(P|G 6%,35)*(F|P 6%,35)

a FOR 5% b FOR 6%EOY CF EOY CF

0 $0.00 0 $0.001 $7,500.00 1 $7,500.002 $8,500.00 2 $8,500.003 $9,500.00 3 $9,500.004 $10,500.00 4 $10,500.005 $11,500.00 5 $11,500.006 $12,500.00 6 $12,500.007 $13,500.00 7 $13,500.008 $14,500.00 8 $14,500.009 $15,500.00 9 $15,500.00

10 $16,500.00 10 $16,500.0011 $17,500.00 11 $17,500.0012 $18,500.00 12 $18,500.0013 $19,500.00 13 $19,500.0014 $20,500.00 14 $20,500.00

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15 $21,500.00 15 $21,500.0016 $22,500.00 16 $22,500.0017 $23,500.00 17 $23,500.0018 $24,500.00 18 $24,500.0019 $25,500.00 19 $25,500.0020 $26,500.00 20 $26,500.0021 $27,500.00 21 $27,500.0022 $28,500.00 22 $28,500.0023 $29,500.00 23 $29,500.0024 $30,500.00 24 $30,500.0025 $31,500.00 25 $31,500.0026 $32,500.00 26 $32,500.0027 $33,500.00 27 $33,500.0028 $34,500.00 28 $34,500.0029 $35,500.00 29 $35,500.0030 $36,500.00 30 $36,500.0031 $37,500.00 31 $37,500.0032 $38,500.00 32 $38,500.0033 $39,500.00 33 $39,500.0034 $40,500.00 34 $40,500.0035 $41,500.00 35 $41,500.00

FW= $1,783,808.45 FW= $2,109,673.85 =FV(5%,35,,-NPV(5%,CF YR 1:CF YR 35)+0) =FV(6%,35,,-NPV(6%,CF YR 1:CF YR 35)+0)

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PROBLEM 2.100

i= 5.00%n= 5

INITIAL CF= -$90,000.00

$30,000.00G= -$3,000.00

PW= $15,173.64 USING INTEREST TABLES THIS IS =-$90,000+$30,000*(P|A 5%,5)-$3,000*(P|G 5%,5)

PW= $15,173.55 USING EXCEL'S NPV FUNCTION THIS IS

=NPV(5%,30000,30000-3000,30000-2*3000,30000-3*3000,30000-4*3000)-90000

PROBLEM 2.101

a i= 6.00%n= 7

INITIAL CF= $0.00

$7,000.00G= -$1,000.00

EQ(t=5)= $31,618.32 USING INTEREST TABLES THIS IS =($7,000*(P|A 6%,7)-$1,000*(P|G 6%,7))*(F|P 6%,5)

b i= 10.00%n= 7

INITIAL CF= $0.00

$7,000.00G= -$1,000.00

EQ(t=5)= $34,329.34 USING INTEREST TABLES THIS IS =($7,000*(P|A 10%,7)-$1,000*(P|G 10%,7))*(F|P 10%,5)

a EOY CF b EOY CF0 $0.00 0 $0.001 $7,000.00 1 $7,000.002 $6,000.00 2 $6,000.003 $5,000.00 3 $5,000.004 $4,000.00 4 $4,000.005 $3,000.00 5 $3,000.006 $2,000.00 6 $2,000.007 $1,000.00 7 $1,000.00

EQ(t=5)= $31,618.22 EQ(t=5)= $34,329.33

=FV(6%,5,,-NPV(6%,CF YR 1:CF YR 7)+0)

=FV(10%,5,,-NPV(10%,CF YR 1:CF YR 7)+0)

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PROBLEM 2.102

i= 12.00%n= 8

INITIAL CF= -$50,000.00

$13,000.00G= -$1,000.00

PW= $107.87 USING INTEREST TABLES THIS IS =-$50,000+$13,000*(P|A 12%,8)-$1,000*(P|G 12%,8)

EOY CF0 -$50,000.001 $13,000.002 $12,000.003 $11,000.004 $10,000.005 $9,000.006 $8,000.007 $7,000.008 $6,000.00

PW= $107.87 USING EXCEL'S NPV FUNCTION THIS IS=NPV(12%,CF YR 1:CF YR 8)-50000

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PROBLEM 2.103

i= 10.00%n= 8

INITIAL CF= -$50,000.00

$13,000.00G= -$1,000.00

A= $623.52 USING INTEREST TABLES THIS IS =-$50,000*(A|P 10%,8)+$13,000-$1,000*(A|G 10%,8)

EOY CF0 -$50,000.001 $13,000.002 $12,000.003 $11,000.004 $10,000.005 $9,000.006 $8,000.007 $7,000.008 $6,000.00

A= $623.32 USING EXCEL'S PMT AND NPV FUNCTIONS THIS IS=PMT(10%,8,-(NPV(10%,CF YR 1:CF YR 8)-50000))

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USING INTEREST TABLES THIS IS =-$50,000*(A|P 10%,8)+$13,000-$1,000*(A|G 10%,8)

USING EXCEL'S PMT AND NPV FUNCTIONS THIS IS=PMT(10%,8,-(NPV(10%,CF YR 1:CF YR 8)-50000))

E12345

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PROBLEM 2.104

i= 8.00%n= 8

INITIAL CF= -$50,000.00

$13,000.00G= -$1,000.00

FW= $12,771.82 USING INTEREST TABLES THIS IS =(-$50,000+$13,000*(P|A 8%,8)-$1,000*(P|G 8%,8))*(F|P 8%,8)

EOY CF0 -$50,000.001 $13,000.002 $12,000.003 $11,000.004 $10,000.005 $9,000.006 $8,000.007 $7,000.008 $6,000.00

FW= $12,771.80 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(8%,8,,-(NPV(8%,CF YR 1:CF YR 8)-50000))

A B C D E F G H I123456

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PROBLEM 2.105

i= 6.00%n= 8

INITIAL CF= -$50,000.00

$13,000.00G= -$1,000.00

FIRST, DETERMINE THE PW OF THE CASH FLOW SERIESPW= $10,885.69 USING INTEREST TABLES THIS IS

=-$50,000+$13,000*(P|A 6%,8)-$1,000*(P|G 6%,8)NOW, DETERMINE THE VALUE OF X FOR THE EQUIVALENT SERIES X, 2X, 3X, …, 8X

PW= $10,885.69 =X*(P|A 6%,8)+X*(P|G 6%,8)$10,885.69 =X*(6.20979+19.84158)$10,885.69 =26.05137*X

X= $417.85

THIS CAN ALSO BE WELL APPROACHED USING SOLVER AS FOLLOWS

X= $417.86 <--SOLVER CHANGED CELL

EOY CF EOY CF0 -$50,000.00 0 01 $13,000.00 1 $417.862 $12,000.00 2 $835.713 $11,000.00 3 $1,253.574 $10,000.00 4 $1,671.435 $9,000.00 5 $2,089.286 $8,000.00 6 $2,507.147 $7,000.00 7 $2,925.008 $6,000.00 8 $3,342.85

PW= $10,885.74 PW= $10,885.74 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION USING EXCEL'S NPV FUNCTION=NPV(6%,CF YR 1:CF YR 8)-50000 =NPV(6%,CF YR 1:CF YR 8)+0

FIRST, DETERMINE THE PW OF THE ORIGINAL CASH FLOW SERIES. THEN, LET X BE ANY VALUE AND SET UP A TABLE OVER 8 YEARS ASSUMING THE VALUE OF X IS CORRECT. DETERMINE THE PW OF THE CASH FLOWS IN THE TABLE USING THE CELL WHERE YOUR VALUE OF X IS STORED. THEN, USE SOLVER TO DETERMINE THE VALUE OF X THAT MAKES THE PW OF THE CASH FLOWS EQUAL TO THE PW VALUE OF THE ORIGINAL CASH FLOW SERIES

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NOW, DETERMINE THE VALUE OF X FOR THE EQUIVALENT SERIES X, 2X, 3X, …, 8X

<--SOLVER CHANGED CELL

<--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION

I12345

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PROBLEM 2.106

i= 6.00%n= 8

INITIAL CF= -$45,000.00

$12,000.00G= -$1,000.00

AMT6= $13,725.46 USING INTEREST TABLES THIS IS =$9,675.90*(F|P 6%,6)

EOY CF0 -$45,000.001 $12,000.002 $11,000.003 $10,000.004 $9,000.005 $8,000.006 $7,000.007 $6,000.008 $5,000.00

AMT6= $13,725.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS

=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000

=FV(6%,6,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000))

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PROBLEM 2.107

i= 6.00%

8 YEARS IN ORIGINAL GRADIENT SERIESINITIAL CF= -$45,000.00

$12,000.00G= -$1,000.00t= 3 YEAR BEFORE ANNUAL SERIES FROM 4 TO 7

4 YEARS IN UNIFORM ANNUAL SERIES

AMT3= $11,524.19 USING INTEREST TABLES THIS IS =$9,675.90*(F|P 6%,3)

A(4-7)= $3,325.77 USING INTEREST TABLES THIS IS =$11,524.19*(A|P 6%,4)

EOY CF0 -$45,000.001 $12,000.002 $11,000.003 $10,000.004 $9,000.005 $8,000.006 $7,000.007 $6,000.008 $5,000.00

PW= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000

AMT3= $11,524.21 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000))

A(4-7)= $3,325.79 USING EXCEL'S PMT FUNCTION THIS IS=PMT(6%,4,-11524.21)

A B C D123

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YEARS IN ORIGINAL GRADIENT SERIES

YEAR BEFORE ANNUAL SERIES FROM 4 TO 7

YEARS IN UNIFORM ANNUAL SERIES

USING INTEREST TABLES THIS IS =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8)USING INTEREST TABLES THIS IS =$9,675.90*(F|P 6%,3)USING INTEREST TABLES THIS IS =$11,524.19*(A|P 6%,4)

USING EXCEL'S NPV FUNCTION THIS IS=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000))USING EXCEL'S PMT FUNCTION THIS IS=PMT(6%,4,-11524.21)

E F G H123

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PROBLEM 2.108

FROM PROBLEM 2.106:i= 6.00%n= 8

INITIAL CF= -$45,000.00

$12,000.00G= -$1,000.00

WE KNOW $10,000

WE KNOW $10,000-7*GPW= $9,675.90 =-$45,000+($10,000-7*G)*(P|A 6%,8)+G*(P|G 6%,8)

=-$45,000+($10,000-7*G)*6.20979+G*19.84158=$17,097.90-23.62695*G

G= $314.13

THEREFORE

$10,000.00 GIVEN IN PROBLEM

$7,801.07 =10000-7*314.13G= $314.13

THIS IS EASIER DONE USING SOLVER AS FOLLOWSFIRST, FIND THE PW OF THE ORIGINAL GRADIENT SERIES

EOY CF0 -$45,000.001 $12,000.002 $11,000.003 $10,000.004 $9,000.005 $8,000.006 $7,000.007 $6,000.008 $5,000.00

G= $314.13 <--SOLVER CHANGED CELL

NOW, SET UP A NEW GRADIENT SERIES THAT HAS THE SAME PW AS THE ORIGINAL SERIES

=A1*(P|A 6%,8)+G*(P|G 6%,8)

=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000

NOW, SET THE GRADIENT AMOUNT "G" TO ANY VALUE AND GO FORWARD AS IF IT IS THE CORRECT VALUE

A B C D E F G H123456

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$10,000.00 GIVEN IN PROBLEM

EOY CF0 -$45,000.001 $7,801.082 $8,115.213 $8,429.344 $8,743.475 $9,057.606 $9,371.747 $9,685.878 $10,000.00

PW= $9,675.95 <--SOLVER TARGET CELL=NPV(6%,CF YR 1:CF YR 8)-45000

NOW, SET UP ANOTHER TABLE OF CASH FLOWS USING THE FACT THAT A8=$10,000, A1=$10,000-7*G, AND A0=-$45,000. THEN, USE SOLVER TO FIND THE PW OF THE SERIES EQUAL TO THAT OF THE ORIGINAL SERIES WHILE CHANGING THE VALUE OF G

A B C D E F G H

5354555657585960616263646566

PROBLEM 2.109

i= 8.00%n= 5

$500.00 G= $100.00

a P= $2,733.60 USING INTEREST TABLES THIS IS =$500*(P|A 8%,5)+$100*(P|G 8%,5)

P= $2,733.60 USING EXCEL'S NPV FUNCTION THIS IS=NPV(C3,500,600,700,800,900)

b A= $684.65 USING INTEREST TABLES THIS IS =$500+$100*(A|G 8%,5)

A= $684.65 USING EXCEL'S PMT FUNCTION THIS IS=PMT(8%,5,-2733.60)

A B C D E F G H1234

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PROBLEM 2.110

i= 12.00%n= 25

$1,000.00G= $200.00

a P= $18,464.07 USING INTEREST TABLES THIS IS =$1,000*(P|A 12%,25)+$200*(P|G 12%,25)

b A= $2,354.17 USING INTEREST TABLES THIS IS =$1,000+$200*(A|G 12%,25)

A= $2,354.18 USING INTEREST TABLES THIS IS =$313,890.35*(A|F 12%,25)

A= $2,354.17 USING EXCEL'S PMT FUNCTION THIS IS=PMT(12%,25,,-313890.35)

A B C D E1234

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PROBLEM 2.111

i= 10.00%n= 10

$7,000.00G= -$300.00

a P= $36,144.59 USING INTEREST TABLES THIS IS =$7,000*(P|A 10%,10)-$300*(P|G 10%,10)

b A= $2,354.17 USING INTEREST TABLES THIS IS =$7,000-$300*(A|G 10%,10)

A= $5,882.80 USING INTEREST TABLES THIS IS =$93,749.66*(A|F 10%,10)

A B C D E1234

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PROBLEM 2.112

i= 8.00%n= 6P= $140,000.00

$11,000.00X= G

PW= USING INTEREST TABLES THIS IS =$11,000*(P|A 8%,6)+G*(P|G 8%,6)=$11,000*4.62288+G*10.52327

SO $140,000.00 =$50,851.68+G*10.52327G=X $8,471.54 =(140000-50851.68)/10.52327

G=X $8,471.54 <--SOLVER CHANGED CELL

EOY CF01 $11,000.002 $19,471.543 $27,943.084 $36,414.625 $44,886.166 $53,357.69

P= $140,000.00 <--SOLVER TARGET CELL=NPV(8%,CF YR 1:CF YR 6)+0

b LAST PAYMENT $53,357.69 =11000+5*8471.54

c i= 8.00%n= 6P= $140,000.00

G=X -$7,500.00

$140,000.00

THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE FIRST PAYMENT IS KNOWN, SOLVE FOR THE GRADIENT PAYMENT G.

THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "G" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF G TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF G.

THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE GRADIENT IS KNOWN, SOLVE FOR THE FIRST PAYMENT A1.

=A1*(P|A 8%,6)-$7,500*(P|G 8%,6)

=A1*4.62288-$7,500*10.52327

A B C D E F G12345

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SO $140,000.00

$47,356.74 =(140000+78924.53)/4.62288

$47,356.75 <--SOLVER CHANGED CELL

EOY CF01 $47,356.752 $39,856.753 $32,356.754 $24,856.755 $17,356.756 $9,856.75

=A1*4.62288-$78,924.53

THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "A1" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF A1 TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF A1.

A B C D E F G

505152535455565758596061

PROBLEM 2.113

i= 10.00%n= 9P= $170,000.00A= $10,000.00 YEARS 1, 2, 3, 4

$11,000.00 YEAR 5X= G

PW= USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,9)+G*(P|G 10%,6)*(P|F 10%,3)=$10,000*5.75902+G*9.68417*0.75131

SO $170,000.00 =$57590.20+G*7.27581G=X= $15,449.80 $15,449.80

G=X= $15,449.68 <--SOLVER CHANGED CELL

EOY CF01 $10,000.002 $10,000.003 $10,000.004 $10,000.005 $25,449.686 $40,899.377 $56,349.058 $71,798.749 $87,248.42

bLAST PAYMENT=

$87,248.42 =10000+5*15449.68

c TOTAL INTEREST PAID=$151,745.27 =SUM(CF YR 0:CF YR 9)-170000

THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE FIRST PAYMENT IS KNOWN, SOLVE FOR THE GRADIENT PAYMENT G.

THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "G" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF G TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF G.

A B C D E F G123456

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PROBLEM 2.114

i= 10.00%n= 5

$10,000.00G= -$1,000.00

P= $31,046.10 USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,5)-$1,000*(P|G 10%,5)

AMT3= $41,322.36 USING INTEREST TABLES THIS IS $31,046.10*(F|P 10%,3)

EOY CF0 $0.001 $10,000.002 $9,000.003 $8,000.004 $7,000.005 $6,000.00

AMT3= $41,322.31 USING EXCEL'S NPV AND FV FUNCTIONS THIS IS

=NPV(10%,7000,6000)+FV(10%,2,,-10000)+FV(10%,1,,-9000)+8000

A B C D E F G H1234

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PROBLEM 2.115

a n= 4

-$10,000.00

$3,000.00G= $1,000.00

PW= $0.00 <--SOLVER TARGET CELLUSING COMPOUND INTEREST FORMULAS THIS IS =-10000+3000*((1+i)^4-1)/(i*(1+i)^4)+1000*(1-(1+4*i)*(1+i)^(-4))/(i^2)

EOY CF0 -$10,000.001 $3,000.002 $4,000.003 $5,000.004 $6,000.00

P= $0.00 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(i%,3000,4000,5000,6000)-10000

b i= 24.8883%

A= $4,226.00 <--SOLVER CHANGED CELL

P= $0.00 <--SOLVER TARGET CELLFORMULAS=-10000+A*((1+0.2489)^4-1)/(0.2489*(1+0.2489)^4)

THIS PROBLEM, IN WHICH THE VALUE OF THE INTEREST RATE IS TO BE FOUND, IS BEST APPROACHED USING SOLVER. THIS IS DUE TO THE DIFFICULTY OF TRYING TO SOLVE ANALYTICALLY FOR THE INTEREST RATE USING FORMULAS OR INTERPOLATION.

BEGIN BY SETTING A CELL TO HOUSE THE INTEREST RATE. SELECT ANY INTEREST RATE FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.

NOW, DEVELOP A FORMULA FOR THE OVERALL PW AS A FUNCTION OF THE INTEREST RATE. THEN, USE SOLVER TO SET THE PW VALUE EQUAL TO 0 BY CHANGING THE INTEREST RATE i.

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE INTEREST RATE FOUND USING SOLVER BELOW IS THE SAME VALUE FOUND ABOVE.

BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE EQUAL ANNUAL INCOMES, "A." SELECT ANY VALUE FOR "A" IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.

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A= $4,226.00 <--SOLVER CHANGED CELL

EOY CF0 -$10,000.001 $4,226.002 $4,226.003 $4,226.004 $4,226.00

P= $0.00 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(24.8883%,4226,4226,4226,4226)-10000

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE EQUAL ANNUAL INCOME "A" FOUND BELOW IS THE SAME VALUE FOUND ABOVE.

A B C D E F G H I44

46474849505152535455565758

PROBLEM 2.116

a P= INR 20,000,000.00i= 5.00%n= 10

INR 2,000,000.00X= G

P= INR 20,000,000.00 USING INTEREST TABLES THIS IS INR 20,000,000.00 =INR 2,000,000*(P|A 5%,10)+G*(P|G 5%,10)INR 20,000,000.00 =INR 2,000,000*7.72173+G*31.65205INR 20,000,000.00 =INR 15,443,460+G*31.65205

G=X= INR 143,957.18 =(20000000-15443460)/31.65205

G=X= INR 143,956.88 <--SOLVER CHANGED CELL

EOY CF0 INR 0.001 INR 2,000,000.002 INR 2,143,956.883 INR 2,287,913.774 INR 2,431,870.655 INR 2,575,827.536 INR 2,719,784.417 INR 2,863,741.308 INR 3,007,698.189 INR 3,151,655.06

10 INR 3,295,611.94

P= INR 20,000,000.00 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,CF YR 1:CF YR 10)+0

b AMT5= INR 12,960,976.54 USING INTEREST TABLES THIS IS

AMT5= INR 12,961,013.55 USING INTEREST TABLES THIS IS

AMT5= INR 12,961,004.03 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,CF YR 6:CF YR 10)

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF G=X FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE.

=INR 20,000,000*(F|P 5%,5)-2,000,000(F|A 5%,5)-143,957.18(P|G 5%,5)(F|P 5%,5)

=INR 2,719,784.41*(P|A 5%,5)+INR 143,956.88*(P|G 5%,5)

A B C D E F G12345

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PROBLEM 2.117

i= 7.00%

EOY -1 0 1 2 3 4 5 6 7 8 9 10CF $1,200 $1,000 $800 $500 $500 $500 $500 $0 -$800 -$800 $0 $1,500

TO FIND THE VALUE OF AMT5,

AMT5= $6,189.74 USING INTEREST TABLES THIS IS

CHECK THIS USING EXCEL'S NPV AND FV FUNCTIONS

AMT5= $6,189.73 USING EXCEL'S NPV AND FV FUNCTIONS THIS IS=NPV(7%,CF YR 6:CF YR 10)+FV(7%,7,,-NPV(7%,CF YR -1:CF YR 5))

=(($1,200-$200*(A|G 7%,3))*(F|A 7%,3)*(P|F 7%,2)+$500*(P|A 7%,4)*(P|F 7%,2)-$800*(F|A 7%,2)*(P|F 7%,9)+$1,500*(P|F 7%,11))*(F|P 7%,6)

A B C D E F G H I J K L M N O123456789

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PROBLEM 2.118

i= 8.00%n= 40

$2,000.00

$1,000.00

$21,000.00

-$1,000.00

FIRST, FIND THE PW OF THE CASH FLOW PROFILE.

G= $500.00

P= $118,139.04 USING INTEREST TABLES THIS IS $118,139.04 =X*(P|A 8%,40)+$500*(P|G 8%,40)$118,139.04 =X*11.92461+$500*126.04220$118,139.04 =11.92461*X+$63,021.10

X= $4,622.20 =(118139.04-63021.1)/11.92461**********OR, RATHER THAN PERFORM THE ABOVE CALCULATIONS, CAN USE SOLVER

G= $500.00

P= $118,139.04 <--SOLVER TARGET CELLUSING INTEREST TABLES THIS IS =X*(P|A 8%,40)+$500*(P|G 8%,40)

**********

=$2,000*(P|A 8%,20)+$1,000*(P|G 8%,20)+($21,000*(P|A 8%,20)-$1,000*(P|G 8%,20))*(P|F 8%,20)

NOW, LET X EQUAL THE FIRST OF 40 AMOUNTS IN A GRADIENT SERIES WITH GRADIENT G=$500. SOLVE FOR THE PW OF THIS GRADIENT SERIES.

BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE FIRST AMOUNT, X. SELECT ANY AMOUNT FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.

NOW, DEVELOP A FORMULA FOR THE PW AS A FUNCTION OF X. THEN, USE SOLVER TO SET THE PW VALUE TO ITS TARGET VALUE BY CHANGING THE VALUE OF X.

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF X FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE.

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ORIGINAL NEWEOY CF CF

0 $0.00 $0.001 $2,000.00 $4,622.182 $3,000.00 $5,122.183 $4,000.00 $5,622.184 $5,000.00 $6,122.185 $6,000.00 $6,622.186 $7,000.00 $7,122.187 $8,000.00 $7,622.188 $9,000.00 $8,122.189 $10,000.00 $8,622.18

10 $11,000.00 $9,122.1811 $12,000.00 $9,622.1812 $13,000.00 $10,122.1813 $14,000.00 $10,622.1814 $15,000.00 $11,122.1815 $16,000.00 $11,622.1816 $17,000.00 $12,122.1817 $18,000.00 $12,622.1818 $19,000.00 $13,122.1819 $20,000.00 $13,622.1820 $21,000.00 $14,122.1821 $21,000.00 $14,622.1822 $20,000.00 $15,122.1823 $19,000.00 $15,622.1824 $18,000.00 $16,122.1825 $17,000.00 $16,622.1826 $16,000.00 $17,122.1827 $15,000.00 $17,622.1828 $14,000.00 $18,122.1829 $13,000.00 $18,622.1830 $12,000.00 $19,122.1831 $11,000.00 $19,622.1832 $10,000.00 $20,122.1833 $9,000.00 $20,622.1834 $8,000.00 $21,122.1835 $7,000.00 $21,622.1836 $6,000.00 $22,122.1837 $5,000.00 $22,622.1838 $4,000.00 $23,122.1839 $3,000.00 $23,622.1840 $2,000.00 $24,122.18

BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE FIRST AMOUNT, X. SELECT ANY AMOUNT FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.

FIRST SOLVE FOR THE PW OF THE ORIGINAL GRADIENT SERIES. THEN, ADJUST THE PW OF THE NEW GRADIENT SERIES WITH FIRST AMOUNT X AND GRADIENT G=500 TO THE PW OF THE ORIGINAL SERIES BY ADJUSTING THE VALUE OF X. NOTE THAT THE VALUE OF X BELOW IS ESSENTIALLY THE SAME AS THE VALUE FOUND ABOVE.

A B C D E F G H I

454647

4950515253545556575859606162636465666768697071727374757677787980818283848586878889909192

P= $118,138.78 $118,138.78 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(8%,NEW CF YR 1: NEW CF YR 40)+CF YR 0

A B C D E F G H I93949596

PROBLEM 2.119

EOY 0 1 2 3 4 5 6 7 8 9 10CF $100 $80 $60 $40 $20 $0 -$20 -$40 -$60 -$80 -$100

i= 18.00%n= 11

$100.00 G= -$20.00

PW= $172.48 USING INTEREST TABLES THIS IS =($100*(P|A 18%,11)-$20*(P|G 18%,11))*(F|P18%,1)

PW= $172.48 USING EXCEL'S FV FUNCTION THIS IS=FV(18%,1,,-NPV(18%,100,80,60,40,20,0,-20,-40,-60,-80,-100))

A B C D E F G H I J K L M N1234567

9101112131415

PROBLEM 2.120

TOTALEOY CF1 CF2 CF3 CF4 CF

0 $800.00 $800.001 $950.00 $0.00 $950.002 $950.00 -$450.00 $500.003 $950.00 -$900.00 $50.004 $950.00 -$1,350.00 -$400.005 -$600.00 -$600.006 -$600.00 -$600.007 -$600.00 -$600.00

A B C D E F G123456789

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PROBLEM 2.121

EOY CF1 CF2 CF3 CF0 -$7,000.00 -$7,000.001 $0.002 $0.003 $0.004 $0.005 $1,850.00 $0.00 $1,850.006 $1,850.00 $200.00 $2,050.007 $1,850.00 $400.00 $2,250.008 $1,850.00 $600.00 $2,450.009 $1,850.00 $800.00 $2,650.00

10 $1,850.00 $1,000.00 $2,850.00

A B C D E F123456789

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PROBLEM 2.122

a (F|G i%,n)=(P|G i%,n)*(F|P i%,n)

b (F|G i%,n)= ((1+i)^n-(1+n*i))/(i^2)

c i= 10.00%n= 5

$0.00G= $1,000.00

USING THE METHOD OF PART a

(F|G i%,n)=(P|G i%,n)*(F|P i%,n)(P|G 10%,5)= 6.8618(F|P 10%,5)= 1.61051

F= $11,051.00 USING INTEREST TABLES THIS IS $1,000*(P|G 10%,5)*(F|P 10%,5)

USING THE METHOD OF PART b

(F|G i%,n)= 11.05100 =((1+0.1)^5-(1+5*0.1))/(0.1^2)

F= $11,051.00 =$1,000.00*11.05100

A B C D E F12345678

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USING INTEREST TABLES THIS IS

G12345678

101112131415161718192021222324

PROBLEM 2.123

FACTOR

i= 7.00%USING 7% FOR EXAMPLE CALCj= 5.00%USING 5% FOR EXAMPLE CALCn= 10USING 10 FOR EXAMPLE CALC

8.59763CHECKS WITH GEOMETRIC SERIES-PRESENT WORTH TABLE

FACTOR

i= 7.00% USING 7% FOR EXAMPLE CALCj= 5.00% USING 5% FOR EXAMPLE CALCn= 10 USING 10 FOR EXAMPLE CALC

16.91284 CHECKS WITH GEOMETRIC SERIES-FUTURE WORTH TABLE

FACTOR

i= 7.00% USING 7% FOR EXAMPLE CALCj= 5.00% USING 5% FOR EXAMPLE CALCn= 10 USING 10 FOR EXAMPLE CALC

1.22411 NOT TABULATED IN APPENDIX A

NOW, COMPLETING THE PROBLEM:

$1,000.00i= 7.00%j= 5.00%

A= $1,224.11=$1,000*1.22411

A= $1,224.13

=$1,000*8.59763*0.14238

A= $1,224.15

=$1,000*16.91284*0.07238

USING A|A1 FACTOR

USING P|A1 FACTOR * A|P FACTOR

=$1,000*(P|A1 7%,5%,10)*(A|P 7%,10)

USING F|A1 FACTOR * A|F FACTOR

=$1,000*(F|A1 7%,5%,10)*(A|F 7%,10)

A B C D E F G H I12

12131415

20212223

252627

293031

PROBLEM 2.124

i= 5.00%n= 30

$7,500.00j= 5.00%

F= $926,130.53 USING INTEREST TABLES THIS IS

**********

EOY CF01 $7,500.00 =$7,500*(1+0.05)^(1-1)2 $7,875.00 =$7,500*(1+0.05)^(2-1)3 $8,268.754 $8,682.195 $9,116.306 $9,572.117 $10,050.728 $10,553.259 $11,080.92

10 $11,634.9611 $12,216.7112 $12,827.5513 $13,468.9214 $14,142.3715 $14,849.4916 $15,591.9617 $16,371.5618 $17,190.1419 $18,049.6420 $18,952.1321 $19,899.7322 $20,894.7223 $21,939.4624 $23,036.4325 $24,188.2526 $25,397.6627 $26,667.5528 $28,000.9229 $29,400.9730 $30,871.02 =$7,500*(1+0.05)^(30-1)

F= $926,130.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(5%,30,,-NPV(5%,CF YR 1:CF YR 30)+0)

=$7,500*(F|A1 5%,5%,30)

A B C D E F G1234

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PROBLEM 2.125

i= 6.00%n= 30

$7,500.00j= 6.00%

F= $1,219,137.30 USING INTEREST TABLES THIS IS

**********

EOY CF01 $7,500.00 =$7,500*(1+0.06)^(1-1)2 $7,950.00 =$7,500*(1+0.06)^(2-1)3 $8,427.004 $8,932.625 $9,468.586 $10,036.697 $10,638.898 $11,277.239 $11,953.86

10 $12,671.0911 $13,431.3612 $14,237.2413 $15,091.4714 $15,996.9615 $16,956.7816 $17,974.1917 $19,052.6418 $20,195.8019 $21,407.5420 $22,692.0021 $24,053.5222 $25,496.7323 $27,026.5324 $28,648.1225 $30,367.0126 $32,189.0327 $34,120.3728 $36,167.5929 $38,337.6530 $40,637.91 =$7,500*(1+0.06)^(30-1)

F= $1,219,137.28 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,30,,-NPV(6%,CF YR 1:CF YR 30)+0)

=$7,500*(F|A1 6%,6%,30)

A B C D E F G1234

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PROBLEM 2.126

i= 5.00%n= 35

$7,500.00j= 8.00%

F= $2,317,332.22 USING ELECTRONIC INTEREST TABLES THIS IS

**********

AGE EOY CF25 026 1 $7,500.00 =$7,500*(1+0.08)^(1-1)27 2 $8,100.00 =$7,500*(1+0.08)^(2-1)28 3 $8,748.0029 4 $9,447.8430 5 $10,203.6731 6 $11,019.9632 7 $11,901.5633 8 $12,853.6834 9 $13,881.9835 10 $14,992.5336 11 $16,191.9437 12 $17,487.2938 13 $18,886.2839 14 $20,397.1840 15 $22,028.9541 16 $23,791.2742 17 $25,694.5743 18 $27,750.1444 19 $29,970.1545 20 $32,367.7646 21 $34,957.1847 22 $37,753.7548 23 $40,774.0549 24 $44,035.9850 25 $47,558.8651 26 $51,363.5652 27 $55,472.6553 28 $59,910.4654 29 $64,703.3055 30 $69,879.5656 31 $75,469.9357 32 $81,507.5258 33 $88,028.1259 34 $95,070.3760 35 $102,676.00 =$7,500*(1+0.08)^(35-1)

F= $2,317,332.23

=$7,500*(F|A1 5%,8%,35)

USING EXCEL'S FV AND NPV FUNCTIONS THIS IS

A B C D E F1234

101112131415161718192021222324252627282930313233343536373839404142434445464748495051

=FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+0)

A B C D E F

PROBLEM 2.127

FIRST, REVIEW THE ORIGINAL PROBLEM 2.126

i= 5.00%n= 35

$7,500.00j= 8.00%

$2,317,332.22

$20,080.69 =2317332.23/115.40101**********

$20,080.17 SOLVER CHANGED CELLORIGINAL NEW

AGE EOY CF AGE EOY CF25 0 25 026 1 $7,500.00 =$7,500*(1+0.08)^(1-1) 26 1 $0.0027 2 $8,100.00 =$7,500*(1+0.08)^(2-1) 27 2 $0.0028 3 $8,748.00 28 3 $0.0029 4 $9,447.84 29 4 $0.0030 5 $10,203.67 30 5 $0.0031 6 $11,019.96 31 6 $0.0032 7 $11,901.56 32 7 $0.0033 8 $12,853.68 33 8 $0.0034 9 $13,881.98 34 9 $0.0035 10 $14,992.53 35 10 $0.0036 11 $16,191.94 36 11 $20,080.1737 12 $17,487.29 37 12 $21,686.5838 13 $18,886.28 38 13 $23,421.5139 14 $20,397.18 39 14 $25,295.2340 15 $22,028.95 40 15 $27,318.8541 16 $23,791.27 41 16 $29,504.3642 17 $25,694.57 42 17 $31,864.7143 18 $27,750.14 43 18 $34,413.8844 19 $29,970.15 44 19 $37,167.0045 20 $32,367.76 45 20 $40,140.3546 21 $34,957.18 46 21 $43,351.5847 22 $37,753.75 47 22 $46,819.7148 23 $40,774.05 48 23 $50,565.2949 24 $44,035.98 49 24 $54,610.51

=$7,500*(F|A1 5%,8%,35)

NOW, SOLVE FOR THE FIRST INVESTMENT ON HIS 36TH BIRTHDAY TO ACHIEVE THE SAME VALUE OF FW AT EOY 60. LET A1 BE THE VALUE OF THE FIRST INVESTMENT AT EOY 36.

=A1*(F|A1 5%,8%,25)

=A1*115.40101

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF A1 FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE.

50 25 $47,558.86 50 25 $58,979.3551 26 $51,363.56 51 26 $63,697.7052 27 $55,472.65 52 27 $68,793.5153 28 $59,910.46 53 28 $74,297.0054 29 $64,703.30 54 29 $80,240.7655 30 $69,879.56 55 30 $86,660.0256 31 $75,469.93 56 31 $93,592.8257 32 $81,507.52 57 32 $101,080.2458 33 $88,028.12 58 33 $109,166.6659 34 $95,070.37 59 34 $117,899.9960 35 $102,676.00 =$7,500*(1+0.08)^(35-1) 60 35 $127,331.99

F= $2,317,332.23 F= $2,317,332.23

SOLVER TARGET CELL

=FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+0)

PROBLEM 2.128

FIRST, REVIEW THE ORIGINAL PROBLEM 2.126

i= 5.00%j= 8.00%n= 35

$7,500.00

F= $2,317,332.23 USING COMPOUND INTEREST FORMULAS THIS IS=7500*(((1+0.05)^35-(1+0.08)^35))/(0.05-0.08)

A= $25,656.82 USING COMPOUND INTEREST FORMULAS THIS IS=2317332.23*(0.05/((1+0.05)^35-1))

A= $25,652.87 USING INTEREST TABLES THIS IS =$2,317,332.23*(A|F 5%,35)

A= $25,656.82

ORIGINAL CHECK NEWAGE EOY CF AGE EOY CF25 0 25 026 1 $7,500.00 26 1 $25,656.8227 2 $8,100.00 27 2 $25,656.8228 3 $8,748.00 28 3 $25,656.8229 4 $9,447.84 29 4 $25,656.8230 5 $10,203.67 30 5 $25,656.8231 6 $11,019.96 31 6 $25,656.8232 7 $11,901.56 32 7 $25,656.8233 8 $12,853.68 33 8 $25,656.8234 9 $13,881.98 34 9 $25,656.8235 10 $14,992.53 35 10 $25,656.8236 11 $16,191.94 36 11 $25,656.8237 12 $17,487.29 37 12 $25,656.8238 13 $18,886.28 38 13 $25,656.8239 14 $20,397.18 39 14 $25,656.8240 15 $22,028.95 40 15 $25,656.8241 16 $23,791.27 41 16 $25,656.82

=$7,500*(F|A1 5%,8%,35)

NOW, SOLVE FOR THE UNIFORM ANNUAL INVESTMENT TO ACHIEVE THE SAME VALUE OF FW AT EOY 60. LET A BE THE VALUE OF THE ANNUAL INVESTMENT.

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF "A" FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE.

A B C D E F G H I1234567

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42 17 $25,694.57 42 17 $25,656.8243 18 $27,750.14 43 18 $25,656.8244 19 $29,970.15 44 19 $25,656.8245 20 $32,367.76 45 20 $25,656.8246 21 $34,957.18 46 21 $25,656.8247 22 $37,753.75 47 22 $25,656.8248 23 $40,774.05 48 23 $25,656.8249 24 $44,035.98 49 24 $25,656.8250 25 $47,558.86 50 25 $25,656.8251 26 $51,363.56 51 26 $25,656.8252 27 $55,472.65 52 27 $25,656.8253 28 $59,910.46 53 28 $25,656.8254 29 $64,703.30 54 29 $25,656.8255 30 $69,879.56 55 30 $25,656.8256 31 $75,469.93 56 31 $25,656.8257 32 $81,507.52 57 32 $25,656.8258 33 $88,028.12 58 33 $25,656.8259 34 $95,070.37 59 34 $25,656.8260 35 $102,676.00 60 35 $25,656.82

F= $2,317,332.23 F= $2,317,332.23

SOLVER TARGET CELL

=FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+CF YR 0)

A B C D E F G H I50515253545556575859606162636465666768697071

EXCELJ K L M N O

50515253545556575859606162636465666768697071

PROBLEM 2.129

P= -$90,000.00i= 5.00%j= -10.00%n= 5

$30,000.00

PW= $17,467.13 USING COMPOUND INTEREST FORMULAS THIS IS=30000*((1-(1-0.1)^5*(1+0.05)^-5)/(0.05+0.1))-90000

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER.

EOY CF0 -$90,000.001 $30,000.002 $27,000.003 $24,300.004 $21,870.005 $19,683.00

PW= $17,467.13 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,CF YR 1:CF YR 5)-90000

=$30,000*(P|A1 5%,-10%,5)-$90,000

A B C D E F123456

101112

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PROBLEM 2.130

FIRST, FIND THE PW OF THE GIVEN CF PROFILE

i= 6.00%n= 8

INIT INV= $45,000.00

$12,000.00G= -$1,000.00

P= $9,675.90 USING INTEREST TABLES THIS IS -$45,000+$12,000(P|A 6%,8)-$1,000(P|G 6%,8)

P= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS

AT THIS POINT, WE KNOW THE PW OF THE CF PROFILE.

i= 6.00%n= 8

INIT INV= $45,000

$10,000

j= -4.04% <--SOLVER CHANGED CELL

P= $9,675.90 <--SOLVER TARGET CELLUSING INTEREST TABLES THIS IS

j= -4.04% <--SOLVER CHANGED CELL

EOY CF0 -$45,000.001 $10,000.002 $9,596.293 $9,208.874 $8,837.105 $8,480.336 $8,137.97

=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000

TO SOLVE FOR THE VALUE OF j, IT IS MUCH EASIER TO USE SOLVER RATHER THAN TO TRY INTERPOLATION OR AN ANALYTICAL SOLUTION

BEGIN BY SETTING THE VALUE OF "j" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF j TO DEVELOP THE CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO EQUAL THE PW OF THE ORIGINAL CF SERIES BY CHANGING j.

-$45,000+$10,000*(P|A1 6%,j%,8)

SEE BELOW FOR TABULATED CASH FLOWS WITH SOLVER USED TO CONFIRM THE ABOVE ANSWER. NOTE THAT THE VALUE OF j FOUND IS EQUAL TO THAT FOUND ABOVE.

A B C D E F G H1234567

91011121314

161718

20212223

2728293031

3536373839404142434445

7 $7,809.438 $7,494.15

PW= $9,675.95 <--SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(6%,CF YR 1:CF YR 8)-45000

A B C D E F G H464748495051

PROBLEM 2.131

i= 5.00%j= 10.00%n= 18

$2,000.00

PW= $52,410.42 USING COMPOUND INTEREST FORMULA THIS IS

FW= $126,131.92 USING EXCEL'S FV FUNCTION THIS IS=FV(5%,18,,-52410.42)

SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER.

EOY CF01 $2,000.002 $2,200.003 $2,420.004 $2,662.005 $2,928.206 $3,221.027 $3,543.128 $3,897.439 $4,287.18

10 $4,715.9011 $5,187.4812 $5,706.2313 $6,276.8614 $6,904.5415 $7,595.0016 $8,354.5017 $9,189.9518 $10,108.94

PW= $52,410.42 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,CF YR 1:CF YR 18)+0

FW= $126,131.96 USING INTEREST TABLES THIS IS =$52,410*(F|P 5%,18)

=$2,000*(P|A1 5%,10%,18)

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PROBLEM 2.132

i= 12.00%j= 15.00%n= 6

$50,000.00

PW= $286,447.62 USING COMPOUND INTEREST FORMULAS THIS IS =50000*((1-(1+0.15)^6*(1+0.12)^-6)/(0.12-0.15))

PW= $286,447.50 USING ELECTRONIC INTEREST TABLES THIS IS

EOY CF01 $50,000.002 $57,500.003 $66,125.004 $76,043.755 $87,450.316 $100,567.86

=$50,000*(P|A1 12%,15%,6)

A B C D E F G12345

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H12345

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PROBLEM 2.133

i= 7.00% COMPOUNDED ANNUALLYj= -40.00% COMPOUNDED ANNUALLYn= 4

$60,000.00

PW= $115,037.72 USING FORMULAS THIS IS =60000*((1-(1-0.4)^4*(1+0.07)^-4)/(0.07-(-0.4)))

EOY CF0 $0.001 $60,000.002 $36,000.003 $21,600.004 $12,960.00

PW= $115,037.72 USING EXCEL'S NPV FUNCTION THIS IS =NPV(7%,60000,36000,21600,12960)+0

=$60,000*(P|A1 7%,-40%,4)

A B C D E F12345

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PROBLEM 2.134

i= 15.00%j= 6.00%n= 20

$1,000.00

PW= $8,933.81 TABLES FROM APPENDIX A

PW= $8,933.81 TABLES FROM PROBLEM 2.123

USING TABULATED CASH FLOWS

EOY CF0 $0.001 $1,000.002 $1,060.003 $1,123.604 $1,191.025 $1,262.486 $1,338.237 $1,418.528 $1,503.639 $1,593.85

10 $1,689.4811 $1,790.8512 $1,898.3013 $2,012.2014 $2,132.9315 $2,260.9016 $2,396.5617 $2,540.3518 $2,692.7719 $2,854.3420 $3,025.60

=$1,000*(P|A1 15%,6%,20)

A B C D E12345

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PROBLEM 2.135

i= 5.00%j= 10.00%n= 5

$1,000.00

PW= $5,237.53 USING EXCEL'S NPV FUNCTION THIS IS=NPV(5%,1000,1000*1.1,1000*1.1^2,1000*1.1^3,1000*1.1^4)

=$1,000*(P|A1 5%,10%,5)

101112

=NPV(5%,1000,1000*1.1,1000*1.1^2,1000*1.1^3,1000*1.1^4)

I12345

101112

PROBLEM 2.136

i= 5.00%j= 15.00%n= 7

$4,000.00

F= $50,116.76 USING INTEREST TABLES THIS IS

F= $50,116.78 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS

=$4,000*(F|A1 5%,15%,7)

=FV(5%,7,,-NPV(5%,4000,4000*1.15,4000*1.15^2,4000*1.15^3,4000*1.15^4,4000*1.15^5,4000*1.15^6))

PROBLEM 2.137

i= 10.00%j= 5.00%n= 6

$9,000.00

=$9,000*(P|A1 10%,5%,6)

=NPV(10%,9000,9000*1.05,9000*1.05^2,9000*1.05^3,9000*1.05^4,9000*1.05^5)

PROBLEM 2.138

i= 10.00%j= 15.00%n= 4

$2,000.00

a PW= $7,783.80 USING INTEREST TABLES THIS IS

PW= $7,783.79 USING EXCEL'S NPV FUNCTION THIS IS=NPV(10%,2000,2000*1.15,2000*1.15^2,2000*1.15^3)

=$2,000*(P|A1 10%,15%,4)

101112131415161718

PROBLEM 2.139

i= 15.00%j= 10.00%n= 5

$14,000.00

a PW= $55,801.76 USING INTEREST TABLES THIS IS

=$14,000*(P|A1 15%,10%,5)

=NPV(15%,14000,14000*1.1,14000*1.1^2,14000*1.1^3,14000*1.1^4)

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PROBLEM 2.140

i= 6.00%j= 15.00%n= 18

$1,500.00 AT BEGINNING OF YEAR 1

FW= $168,206.35 USING INTEREST TABLES THIS IS

FW= $168,206.35 USING INTEREST TABLES FROM PROBLEM 2.123

EOY CF0 $1,500.001 $1,725.002 $1,983.753 $2,281.314 $2,623.515 $3,017.046 $3,469.597 $3,990.038 $4,588.539 $5,276.81

10 $6,068.3411 $6,978.5912 $8,025.3813 $9,229.1814 $10,613.5615 $12,205.5916 $14,036.4317 $16,141.9018 $0.00

FW= $168,206.36 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,18+1,,-NPV(6%,CF YR 0:CF YR 18))

NOTE THAT THE WORDING OF THIS PROBLEM IMPLIES THE 18 DEPOSITS START AT BIRTH (BEGINNING OF YEAR 1) AND CONTINUE THROUGH BEGINNING OF YEAR 18. THEN, THE AMOUNT AT THE END OF YEAR 18 IS REQUESTED.

=$1,500*(F|A1 6%,15%,18)*(F|P 6%,1)

A B C D E F G H12

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PROBLEM 2.141

i= 15.00%j= 10.00%n= 5

$140,000.00

PW= $558,017.60 USING INTEREST TABLES FROM PROBLEM 2.123

EOY CF0 $0.001 $140,000.002 $154,000.003 $169,400.004 $186,340.005 $204,974.00

=$140,000*(P|A1 15%,10%,5)

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PROBLEM 2.142

i= 11.00%

a LABOR MATERIAL OVERHEAD TOTALj= -5.00% 4.00% 8.00%

$2,000,000.00 $3,000,000.00 $1,600,000.00EOY

0 $0.00 $0.00 $0.00 $0.001 $2,000,000.00 $3,000,000.00 $1,600,000.00 $6,600,000.002 $1,900,000.00 $3,120,000.00 $1,728,000.00 $6,748,000.003 $1,805,000.00 $3,244,800.00 $1,866,240.00 $6,916,040.004 $1,714,750.00 $3,374,592.00 $2,015,539.20 $7,104,881.205 $1,629,012.50 $3,509,575.68 $2,176,782.34 $7,315,370.526 $1,547,561.87 $3,649,958.71 $2,350,924.92 $7,548,445.517 $1,470,183.78 $3,795,957.06 $2,538,998.92 $7,805,139.75

b P= $8,295,499.60 $15,693,016.73 $9,307,846.73 $33,296,363.05 USING EXCEL'S NPV FUNCTION, EACH COLUMN IS=NPV(11%,CF YR 1:CF YR 7)+0

P= $8,295,500.00 $15,693,030.00 $9,307,840.00 $33,296,370.00USING INTEREST TABLES FROM PROBLEM 2.123

c A= $7,065,996.66 USING EXCEL'S PMT FUNCTION THIS IS=PMT(11%,7,-33296363.05)

A= $7,066,155.64 USING INTEREST TABLES THIS IS =$33,296,370.00*(A|P 11%,7)

NOTE! TABLES DO NOT SUPPORT THIS LEVEL OF PRECISION

IN THIS PROBLEM, IT IS MUCH EASIER TO USE A SPREADSHEET AND TO KEEP LABOR, MATERIAL, AND OVERHEAD SEPARATE UNTIL COMBINED.

=$2,000,000.00*(P|A1 11%,-5%,7)

=$3,000,000.00*(P|A1 11%,4%,7)

=$1,600,000.00*(P|A1 11%,8%,7)

A B C D E F12

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PROBLEM 2.143

i= 8.00%j= 5.00%n= 10

SALARY $70,000.00% DEPOSITED 10.00%

$7,000.00

FW= $123,673.76 USING INTEREST TABLES THIS IS

FW= $123,673.76 TABLES FROM PROBLEM 2.123

EOY CF0 $0.001 $7,000.002 $7,350.003 $7,717.504 $8,103.385 $8,508.546 $8,933.977 $9,380.678 $9,849.709 $10,342.19

10 $10,859.30

FW= $123,673.75 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(8%,10,,-NPV(8%,CF YR 1:CF YR 10)+0)

=$7,000*(F|A1 8%,5%,10)

A B C D E F G H1234567

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PROBLEM 2.144

i= 15.00%j= 10.00%n= 5P= $50,000.00

$12,544.41 =50000/3.98584

a SMALLEST PAYMENT $0.00

b LARGEST PAYMENT $18,366.27 =12544.41*(1+0.1)^4

$12,544.41 SOLVER CHANGED CELL

EOY CF0

a 1 $12,544.412 $13,798.863 $15,178.744 $16,696.61

b 5 $18,366.28

P= $50,000.00 SOLVER TARGET CELLUSING EXCEL'S NPV FUNCTION THIS IS=NPV(15%,CF YR 1:CF YR 5)+0

=A1*(P|A1 15%,10%,5)

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. WILL USE SOLVER TO FIND VALUE OF A1.

BEGIN BY DEDICATING A CELL FOR A1 AND LET IT TAKE ON ANY VALUE AS IF IT WERE CORRECT. IT WILL BE CHANGED TO THE CORRECT VALUE WHEN SOLVER IS USED.

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PROBLEM 2.145

i= 6.00%j= 4.00%n= 5

$15,000.00

FW= $91,179.45 TABLES FROM APPENDIX A

EOY CF0 $0.001 $15,000.002 $15,600.003 $16,224.004 $16,872.965 $17,547.88

FW= $91,179.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS=FV(6%,5,,-NPV(6%,CF YR 1:CF YR 5)+0)

=$15,000*(F|A1 6%,4%,5)

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PROBLEM 2.146

TO GO FROM NOMINAL ANNUAL TO EFFECTIVE ANNUAL

NOMINAL ANNUAL INTEREST RATE r= 10.000% USED r=10% FOR EXAMPLE(E.G., 10.000%)COMPOUNDING PERIODS PER YEAR m= 4 USED m=4 FOR EXAMPLE(E.G., 4 FOR QUARTERLY)

EFFECTIVE ANNUAL INTEREST RATE 10.381%

=(1+0.1/4)^4-1

EFFECTIVE ANNUAL INTEREST RATE 10.381%

=EFFECT(10%,4)

TO GO FROM EFFECTIVE ANNUAL TO NOMINAL ANNUAL

EFFECTIVE ANNUAL INTEREST RATE 10.381%(E.G., 10.381%)COMPOUNDING PERIODS PER YEAR m= 4 USED m=4 FOR EXAMPLE(E.G., 4 FOR QUARTERLY)

NOMINAL ANNUAL INTEREST RATE r= 10.000% USED r=10% FOR EXAMPLE

=4*((1+0.10381)^(1/4)-1)

USING EXCEL'S EFFECT FUNCTION THIS IS

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PROBLEM 2.147

i= 0.75% PER MONTHn= 480 MONTHSF= $2,000,000.00

A= $427.23 USING COMPOUND INTEREST FORMULAS THIS IS=2000000*(0.0075/((1+0.0075)^480-1))

A= $427.22 USING INTEREST TABLES THIS IS =$2,000,000*(A|F 0.75%,480)

A= $427.23 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.75%,480,,-2000000)

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PROBLEM 2.148

P= $12,000.00i= 0.75% PER MONTHA= $400.00 PER MONTH

n= 34.1129207 MONTHS USE 35 MONTHSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(0.75%,-400,12000)

CAN ALSO USE SOLVER TO FIND n

n= 34.1129208 <--SOLVER CHANGED CELL USE 35 MONTHS

A= $400.00 <--SOLVER TARGET CELLUSING EXCEL'S PMT FUNCTION THIS IS=PMT(0.75%,n,-12000)

EOY CF PW

01 $400.00 $397.02 2 $400.00 $791.09 3 $400.00 $1,182.22 4 $400.00 $1,570.44 5 $400.00 $1,955.78 6 $400.00 $2,338.24 7 $400.00 $2,717.86 8 $400.00 $3,094.65 9 $400.00 $3,468.63

10 $400.00 $3,839.83 11 $400.00 $4,208.27 12 $400.00 $4,573.97 13 $400.00 $4,936.94 14 $400.00 $5,297.21 15 $400.00 $5,654.80 16 $400.00 $6,009.73 17 $400.00 $6,362.01 18 $400.00 $6,711.67 19 $400.00 $7,058.73 20 $400.00 $7,403.21 21 $400.00 $7,745.12 22 $400.00 $8,084.49 23 $400.00 $8,421.33 24 $400.00 $8,755.66 25 $400.00 $9,087.50 26 $400.00 $9,416.88 27 $400.00 $9,743.80 28 $400.00 $10,068.28 29 $400.00 $10,390.36 30 $400.00 $10,710.03 31 $400.00 $11,027.33 32 $400.00 $11,342.26

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33 $400.00 $11,654.85 34 $400.00 $11,965.11 35 $400.00 $12,273.06 FIRST PW OF >= $12,00036 $400.00 $12,578.72 37 $400.00 $12,882.11 38 $400.00 $13,183.23 39 $400.00 $13,482.12 40 $400.00 $13,778.78

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PROBLEM 2.149

a r= 10.00%m= 2

ieff= 10.2500% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.1/2)^2-1

ieff= 10.2500% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10%,2)

b r= 10.00%m= 3

c r= 10.00%m= 4

d r= 10.00%m= 6

e r= 10.00%m= 12

ieff= 10.4713% USING COMPOUND INTEREST FORMULAS THIS IS10.4713%

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PROBLEM 2.150

a r= 5.00%m= 2

b r= 5.00%m= 3

c r= 5.00%m= 4

d r= 5.00%m= 6

e r= 5.00%m= 12

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PROBLEM 2.151

r= 6.00% PER YEARm= 12i= 0.50% PER MONTHn= 60 MONTHSP= $50,000.00

A= $966.50 USING INTEREST TABLES THIS IS =$50,000*(A|P 0.50%,60)

A= $966.64 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.5%,60,-50000)

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PROBLEM 2.152

a i= 0.50% PER MONTHn= 30 MONTHLY PAYMENTSP= $500.00

A= $17.99 USING INTEREST TABLES THIS IS =$500*(A|P 0.50%,30)

b i= 0.50% PER MONTHn= 30 MONTHLY PAYMENTSP= $500.00

DELAY= 12 MONTHS

AMT12MO= $530.84 USING INTEREST TABLES THIS IS =$500.00*(F|P 0.5%,12)

A= $19.10 USING INTEREST TABLES THIS IS =$530.84*(A|P 0.50%,30)

AMT12MO= $530.84 USING EXCEL'S FV FUNCTION THIS IS=FV(0.5%,12,,-C16)

A= $19.10 USING EXCEL'S PMT FUNCTION THIS IS=PMT(0.5%,30,-530.84)

FIRST, DETERMINE THE FUTURE WORTH OF THE ORIGINAL $500 AFTER 12 MONTHS. THEN, DETERMINE THE MONTHLY PAYMENT

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PROBLEM 2.153

r= 6.000%m= 2

YRS= 10P= $4,000.00

FW= $7,224.44 USING COMPOUND INTEREST FORMULAS THIS IS=4000*(1+0.06/2)^(2*10)

FW= $7,224.44 USING EXCEL'S FV FUNCTION THIS IS=FV(0.06/2,2*10,,-4000)

OR, CAN USE THE EFFECTIVE RATE AS FOLLOWS

6.090% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(6%,2)

FW= $7,224.44 USING COMPOUND INTEREST FORMULAS THIS IS=4000*(1+0.0609)^10

FW= $7,224.44 USING EXCEL'S FV FUNCTION THIS IS=FV(6.09%,10,,-4000)

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PROBLEM 2.154

r= 5.000%m= 4

YRS= 4F= $10,000.00

P= $8,197.50 USING INTEREST TABLES THIS IS=$10,000*(P|F 1.25%,16)

P= $8,197.46 USING EXCEL'S PV FUNCTION THIS IS=PV(0.05/4,4*4,,-10000)

OR, CAN USE THE EFFECTIVE RATE AS FOLLOWS

5.09453% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.05/4)^4-1

P= $8,197.46 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.0509453)^-4

P= $8,197.46 USING EXCEL'S PV FUNCTION THIS IS=PV(5.09453%,4,,-10000)

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PROBLEM 2.155

a ANNUALLYr= 7.000%m= 1

YRS= 5P= $10,000.00

F= $14,025.52 USING COMPOUND INTEREST FORMULAS THIS IS=10000*(1+0.07/1)^(1*5)

F= $14,025.52 USING EXCEL'S FV FUNCTION THIS IS=FV(0.07/1,1*5,,-10000)

b QUARTERLYr= 7.000%m= 4

YRS= 5P= $10,000.00

F= $14,147.80 USING INTEREST TABLES THIS IS=$10,000*(F|P 1.75%,20)

c MONTHLYr= 7.000%m= 12

YRS= 5P= $10,000.00

F= $14,176.00 USING ELECTRONIC INTEREST TABLES THIS IS=$10,000*(F|P 7/12%,60)

d DAILYr= 7.000%m= 365

YRS= 5P= $10,000.00

F= $14,190.00 USING ELECTRONIC INTEREST TABLES THIS IS=$10,000*(F|P 7/365%,1825)

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PROBLEM 2.156

a ANNUALLYr= 6.000%m= 1

YRS= 8F= $20,000.00

P= $12,548.25 USING COMPOUND INTEREST FORMULAS THIS IS=20000*(1+0.06/1)^(-1*8)

P= $12,548.20 USING INTEREST TABLES THIS IS=$20,000*(P|F 6%,8)

P= $12,548.25 USING EXCEL'S FV FUNCTION THIS IS=PV(0.06/1,1*8,,-20000)

b SEMI-ANNUALLYr= 6.000%m= 2

YRS= 8F= $20,000.00

P= $12,463.40 USING INTEREST TABLES THIS IS=$20,000*(P|F 3%,16)

c QUARTERLYr= 6.000%m= 4

YRS= 8F= $20,000.00

d MONTHLYr= 6.000%m= 12

YRS= 8F= $20,000.00

e WEEKLY

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r= 6.000%m= 52

YRS= 8F= $20,000.00

P= $12,379.00 USING INTEREST TABLES THIS IS=$20,000*(P|F 0.6/52%,416)

f DAILYr= 6.000%m= 365

YRS= 8F= $20,000.00

g HOURLYr= 6.000%m= 8760

YRS= 8F= $20,000.00

h MINUTELYr= 6.000%m= 525600

YRS= 8F= $20,000.00

i SECONDLYr= 6.000%m= 31536000

YRS= 8F= $20,000.00

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PROBLEM 2.157

BUILDING THE ACCOUNTr= 8.000% COMPOUNDED MONTHLYm= 12 MONTHS PER YEAR

YRS= 20A= $400.00 PER MONTH

DETERMINE AMOUNT IN ACCOUNT AT END OF 20 YEARS, END OF MONTH 240F(240)= $235,608.00 USING INTEREST TABLES THIS IS

$400*(F|A 8/12%,240)F(240)= $235,608.17 USING EXCEL'S FV FUNCTION THIS IS

=FV(0.08/12,12*20,-400)

DETERMINE AMOUNT IN ACCOUNT AT END OF MONTH 251, ONE MONTH BEFORE 1ST WITHDRAWAL AT END OF MONTH 252

1ST WDL 252 MONTH 252 IS FIRST WITHDRAWALr= 8.000% COMPOUNDED MONTHLYm= 12 MONTHS PER YEAR

YRS= 15

F(251)= $253,474.15 USING INTEREST TABLES THIS IS=$235608.00*(F|P 8/12%,11)

F(251)= $253,473.70 USING EXCEL'S FV FUNCTION THIS IS =FV(0.08/12,11,,-235608.17)

a A= $2,423.21 USING INTEREST TABLES THIS IS=$253,474.15*(A|P 8/12%,12*15)

A= $2,422.33 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.08/12,12*15,-253473.7)

b A= $1,689.82 CALCULATING MONTHLY INTEREST ONLY=(0.08/12)*253473.7

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PROBLEM 2.158

a BUILDING THE ACCOUNT FOR 30 YEARSr= 8.000%m= 12 MONTHS PER YEAR

YRS= 30A= $300.00 PER MONTH

AMT360= $447,120.00 USING INTEREST TABLES THIS IS=$300*(F|A 8/12%,360)

AMT360= $447,107.83 USING EXCEL'S FV FUNCTION THIS IS=FV(8%/12,12*30,-300)

b LETTING THE ACCOUNT BUILD FOR 7 MORE QUARTERSr= 12.000%m= 4 QTRS/YEAR

YRS= 15

AMT7QTR= $549,899.47 USING INTEREST TABLES THIS IS=$447,120*(F|P 3%,7)

AMT7QTR= $549,886.24 USING EXCEL'S FV FUNCTION THIS IS=FV(12%/4,7,,-C13)

c WITHDRAWING FROM THE ACCOUNTSTARTING 2 YEARS AFTER LAST DEPOSIT

A= $19,867.87 USING INTEREST TABLES THIS IS=$549,899.47*(A|P 3%,60)

A= $19,869.02 USING EXCEL'S PMT FUNCTION THIS IS=PMT(12%/4,4*15,-549886.24)

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PROBLEM 2.159

MONTHLY RATE= 2.50%m= 12P= $2,000.00

YRS= 2

a NOM ANN RATE= 30.000% =2.5%*12

b EFF ANN RATE= 34.4889% USING COMPOUND INTEREST FORMULAS THIS IS=(1+30%/12)^12-1

EFF ANN RATE= 34.4889% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(30%,12)

c F= $3,617.46 USING INTEREST TABLES THIS IS=$2,000*(F|P 2.5%,24)

F= $3,617.45 USING EXCEL'S FV FUNCTION THIS IS=FV(2.5%,12*2,,-2000)

d F= $3,617.46 USING ELECTRONIC INTEREST TABLES THIS IS=$2,000*(F|P 34.4889%,2)

e INTEREST= $1,617.45 =3617.45-2000.00

f A= $111.82 USING INTEREST TABLES THIS IS=$2,000*(A|P 2.5%,24)

A= $111.83 USING EXCEL'S PMT FUNCTION THIS IS=PMT(2.5%,12*2,-2000)

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PROBLEM 2.160

m= 12 MONTHS PER YEARn= 40 MONTHSA= $250.00 PER MONTHF= $12,000.00

r= 10.932% <--SOLVER CHANGED CELL

F= $12,000.00 <--SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(r%/12,40,-250)

NOW, KNOWING r, PROCEED WITH THE PROBLEM

a 0.911% =10.932%/12

b r= 10.932% FOUND USING SOLVER ABOVE

c 11.497% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.10932/12)^12-1

11.497% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(10.932%,12)

SINCE THIS PROBLEM SEEKS TO DETERMINE AN INTEREST RATE, IT IS BEST TO USE SOLVER TO AVOID A DIFFICULT ANALYTICAL SOLUTION OR INTERPOLATION.

BEGIN BY ESTABLISHING A CELL FOR THE VALUE OF THE NOMINAL RATE r AND USE ANY VALUE, ASSUMING IT IS CORRECT. IT WILL LATER BE CHANGED BY SOLVER TO THE CORRECT VALUE.

imonthly=

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PROBLEM 2.161

m= 12YRS= 5

A= $501.49P= $20,000.00

r= 17.412% <--SOLVER CHANGED CELL

P= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=PV(r/12,12*5,-20000)

NOW, KNOWING r, PROCEED WITH THE PROBLEM

a 1.451% =17.412%/12

b r= 17.412% FOUND USING SOLVER ABOVE

18.871% USING EXCEL'S EFFECT FUNCTION THIS IS=EFFECT(17.412%,12)

SINCE THIS PROBLEM SEEKS TO DETERMINE AN INTEREST RATE, IT IS BEST TO USE SOLVER TO AVOID A DIFFICULT ANALYTICAL SOLUTION OR INTERPOLATION.

BEGIN BY ESTABLISHING A CELL FOR THE VALUE OF THE NOMINAL RATE r AND USE ANY VALUE, ASSUMING IT IS CORRECT. IT WILL LATER BE CHANGED BY SOLVER TO THE CORRECT VALUE.

imonthly=

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PROBLEM 2.162

a REFUND= $1,000.00INT RATE= 3.000% PER WEEKINT PAID= $30.00 =1000*0.03

m= 52 WEEKS/YR

CASH RCVD= $970.00 =1000-30

b WEEKLY INT= 3.093% =30/970

c r= 160.825% =3.093%*52

d 387.382% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.03093)^52-1

387.382% USING EXCEL'S EFFECT FUNCTION387.384%

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PROBLEM 2.163

PLAN 1 PLAN 2

r= 7.000% r= 6.625%m= 12 m= 12

YRS= 30 YRS= 15P= $600,000.00 P= $600,000.00

a A= $3,990.00 USING INTEREST TABLES THIS IS=$600,000*(A|P 7/12%,360)

A= $3,991.81 USING EXCEL'S PMT FUNCTION THIS IS=PMT(7%/12,12*30,-600000)

b A= $5,268.00 USING INTEREST TABLES THIS IS=$600,000*(A|P 6.625/12%,180)

A= $5,267.96 USING EXCEL'S PMT FUNCTION THIS IS=PMT(6.625%/12,12*15,-600000)

7.229% USING EXCEL'S EFFECT FUNCTION=EFFECT(7%,12)

d 6.830% USING COMPOUND INTEREST FORMULAS THIS IS=(1+0.06625/12)^12-1

6.830% USING EXCEL'S EFFECT FUNCTION=EFFECT(6.625%,12)

e INT PAID= $837,053.39 =3991.81*12*30-600000

f INT PAID= $348,233.27 =5267.96*12*15-600000

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PROBLEM 2.164

r= 6.00% PER YEARm= 4 CMPDGS PER YEARn= 60 MONTHSk= 12 PAYMENTS PER YEARP= $50,000.00

FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (MONTH)

i= 0.49752063% PER MONTHUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.06/4)^(4/12)-1

NOW, PROCEED WITH THE REST OF THE PROBLEM

A= $965.95 USING COMPOUND INTEREST FORMULAS THIS IS=50000*(0.0049752063*(1+0.0049752063)^60)/((1+0.0049752063)^60-1)

A= $966.00 USING INTEREST TABLES THIS IS=$50,000*(A|P 0.49752063%,60)

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=50000*(0.0049752063*(1+0.0049752063)^60)/((1+0.0049752063)^60-1)

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PROBLEM 2.165

NOTE! IF YOU HAVE THE FIRST PRINTING, SEE PROBLEM 2.167 FOR SOLUTION

FOLLOWING IS THE SOLUTION TO PROBLEM 2.165 IN LATER PRINTINGS

r= 6.000%m= 4 QUARTERS PER YEARk= 12 DEPOSITS PER YEARA= $150.00 PER MONTHF= $20,000.00

n= 102.5293974279 MONTHSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(0.4975206%,150,,-20000)

OR COULD USE SOLVER AS FOLLOWS

F= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(0.4975206,n,-150)

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NOTE! IF YOU HAVE THE FIRST PRINTING, SEE PROBLEM 2.167 FOR SOLUTION

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PROBLEM 2.166

r= 7.000% PER YEARm= 12 MONTHS PER YEARk= 4 DEPOSITS PER YEARA= $300.00 PER QUARTERF= $15,000.00

FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (QUARTER)

i= 1.760% PER QUARTERUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.07/12)^(12/4)-1

n= 36.18126076 QUARTERSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(1.760%,300,,-15000)

n= 36.18126076 <--SOLVER CHANGED CELLQUARTERS

F= $15,000.00 <--SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(1.760%,n,-300)

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PROBLEM 2.167 (ALSO PROBLEM 2.165 IN FIRST PRINTING)

r= 7.000%m= 4 QUARTERS PER YEARk= 12 DEPOSITS PER YEARA= $100.00 PER MONTHF= $15,000.00

n= 108.23482720625 MONTHSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(0.57996326%,100,,-15000)

F= $15,000.00 <--SOLVER TARGET CELLUSING EXCEL'S FV FUNCTION THIS IS=FV(0.57996326,n,-100)

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PROBLEM 2.168

r= 6.000% PER YEARm= 12 MONTHS PER YEARk= 4 WITHDRAWALS PER QTRA= $1,200.00 PER QUARTERP= $20,000.00

FIRST, CALCULATE THE INTEREST RATE PER CASH FLOW PERIOD (QUARTER)

i= 1.508% PER QUARTERUSING COMPOUND INTEREST FORMULAS THIS IS=(1+0.06/12)^(12/4)-1

n= 19.33837953 QUARTERSUSING EXCEL'S NPER FUNCTION THIS IS=NPER(1.508%,1200,-20000)

n= 19.33837953 <--SOLVER CHANGED CELL QUARTERS

P= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS=FV(1.508%,n,-1200)

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PROBLEM 2.169

r= 6.000% PER YEARm= 4 QUARTERSk= 12 MONTHSA= $400.00 PER MONTHP= $20,000.00

n= 57.6340855 USING EXCEL'S NPER FUNCTION THIS IS =NPER(0.004975206,400,-20000)OR 57 WHOLE MONTHS

OR, COULD USE SOLVER TO FIND n

n= 57.6340855 <--SOLVER CHANGED CELLMONTHS

P= $20,000.00 <--SOLVER TARGET CELLUSING EXCEL'S PV FUNCTION THIS IS =PV(0.004975206,n,-400)

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PROBLEM 2.170

FOR n PERIODS FROM EQ 2.9

FOR m PERIODS FROM EQ 2.9

FOR m PERIODS FROM EQ 2.8

a FOR n+m PERIODS FROM EQ 2.9

(P|F i%,n)*(P|F i%,m) EQ 2.53 - QED

b FOR n-m PERIODS FROM EQ 2.9

(P|F i%,n)*(F|P i%,m) EQ 2.54 - QED

c FOR nm PERIODS FROM EQ 2.9

EQ 2.55 - QED

d FOR nm PERIODS FROM EQ 2.9

EQ 2.56 - QED

(P|F i%,n)=(1+i)-n

(P|F i%,m)=(1+i)-m

(F|P i%,m)=(1+i)m

(P|F i%,n+m)=(1+i)-(n+m)

(P|F i%,n+m)=(1+i)-(n+m)= (1+i)-n*(1+i)-m=

(P|F i%,n+m)=(1+i)-(n+m)=

(P|F i%,n-m)=(1+i)-(n-m)

(P|F i%,n-m)=(1+i)-(n-m)= (1+i)-n*(1+i)m=

(P|F i%,n-m)=(1+i)-(n-m)=

(P|F i%,nm)=(1+i)-nm

(P|F i%,nm)=(1+i)-(nm)= ((1+i)-n)m=

(P|F i%,nm)=(1+i)-(nm)= (P|F i%,n)m

(P|F i%,nm)=(1+i)-nm

(P|F i%,nm)=(1+i)-(nm)= ((1+i)-m)n=

(P|F i%,nm)=(1+i)-(nm)= (P|F i%,m)n

A B C D123456789

1011121314151617181920212223242526272829303132

PROBLEM 2.171

2.57 a $0 0 1

b (P|G i%,n)=

(P|G i%,1)=

2.58 a $0 0 1

b (A|G i%,n)=

(A|G i%,1)=

2.59 a $A=$P*(1+i)$F=$P*(1+i)

b (A|P i%,n)=

(A|P i%,1)=

(F|P i%,n)=

(F|P i%,1)=

2.6 a $F

b (A|F i%,n)=

(A|F i%,1)=

(F|A i%,n)=

(F|A i%,1)=

(1-(1+n*i)*(1+i)-n)/(i2)

(1-(1+i)*(1+i)-1)/(i2)=0

(1/i)-(n/i)*(i/((1+i)n-1))

(1/i)-(1/i)*(i/((1+i)1-1))=0

(i*(1+i)n)/((1+i)n-1)

(i*(1+i)1)/((1+i)1-1)=1+i

(1+i)n

(1+i)1=1+i

i/((1+i)n-1)

i/((1+i)1-1)=1

((1+i)n-1)/i

((1+i)1-1)/i=1

A B C D123456789

1011121314151617181920212223242526272829303132333435363738394041424344454647

FIRST YEAR OF A GRADIENT SERIES IS $0

E123456789

1011121314151617181920212223242526272829303132333435363738394041424344454647

PROBLEM 2.172

a r= 5.000%m= 1

b r= 5.000%m= 365

c r= 5.000%m= INFINITE 10000000 USING A VERY LARGE NUMBER

5.127% USING EXCEL'S EFFECT FUNCTION THIS ISASSUME VERY LARGE m=EFFECT(5%,10000000)

5.127% USING EQUATION 2.A.1

910111213

1718192021

PROBLEM 2.173

a r= 10.000%m= 1

b r= 10.000%m= 365

10.516% USING COMPOUND INTEREST FORMULAS THIS IS10.516%

c r= 10.000%m= INFINITE 10000000 USING A VERY LARGE NUMBER

10.517% USING EXCEL'S EFFECT FUNCTION THIS ISASSUME VERY LARGE m=EFFECT(10%,10000000)

10.517% USING EQUATION 2.A.1

910111213

1718192021

PROBLEM 2.174

r= 10.000% COMPOUNDED CONTINUOUSLYYRS= 5

P= $10,000.00m= 10,000,000 LARGE NUMBER OF CPDG PERIODS PER YEAR

F= $16,487.21 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS=C5*EXP(C3*C4)

F= $16,487.20 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS

F= $16,487.21 USING EXCEL'S FV FUNCTION THIS ISASSUME VERY LARGE m=FV(10%/10000000,5*10000000,,-10000)

=$10,000*(F|P 10%,5)∞

A B C D E F G H123456789

121314

USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS

USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS

I123456789

121314

PROBLEM 2.175

r= 15.000% COMPOUNDED CONTINUOUSLYYRS= 4

F= $15,000.00m= 10000000 LARGE NUMBER OF CPDG PERIODS PER YEAR

P= $8,232.17 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS=15000*EXP(-15%*4)

P= $8,232.15 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS

P= $8,232.17 USING EXCEL'S PV FUNCTION THIS ISASSUME VERY LARGE m=PV(15%/10000000,4*10000000,,-15000)

=$15,000*(P|F 15%,4)∞

A B C D E F G H I J123456789

121314

PROBLEM 2.176

r= 5.000% PER 6 MONTHSn= 14 6 MONTH PERIODSA= $500.00 PER 6 MONTHS

a F= $9,886.20 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS$9,886.20

F= $9,886.20 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS

b P= $4,909.34 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS=500*(EXP(5%*14)-1)/(EXP(5%*14)*(EXP(5%)-1))

c P= $4,909.34 USING CONTINUOUS COMPOUNDING INTEREST FORMULAS THIS IS=9886.2*EXP(-5%*14)

NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r MUST MATCH THE PERIOD

=$500*(F|A 5%,14)∞

=$500*(P|A 5%,14)∞

=$9,886.2*(P|F 5%,14)∞

A B C D E F G H I12

456789

13141516

18192021

456789

13141516

18192021

PROBLEM 2.177

r= 5.000% PER 6 MONTHSn= 14 6 MONTH PERIODSA= $500.00 PER 6 MONTHSG= $100.00 PER 6 MONTHS

a F= $21,144.77

=$500*19.7724+$100*55.90849*2.01375

b P= $10,500.19

=$500*9.81868+$100*55.90849

P= $10,500.28

=$21,144.77*0.49659

c A= $1,069.50

=$21,144.77*0.05058

TABLE TO ILLUSTRATE AND CHECK ANSWER TO a AND b

PERIOD PYT FW PW01 $500.00 $957.77 $475.612 $600.00 $1,093.27 $542.903 $700.00 $1,213.28 $602.504 $800.00 $1,318.98 $654.985 $900.00 $1,411.48 $700.926 $1,000.00 $1,491.82 $740.827 $1,100.00 $1,560.97 $775.168 $1,200.00 $1,619.83 $804.389 $1,300.00 $1,669.23 $828.92

10 $1,400.00 $1,709.96 $849.1411 $1,500.00 $1,742.75 $865.4212 $1,600.00 $1,768.27 $878.1013 $1,700.00 $1,787.16 $887.4814 $1,800.00 $1,800.00 $893.85

FOR PERIOD 8 =1200*EXP(0.05*(14-8))=1200*EXP(-0.05*8)

SUM $21,144.79 $10,500.19

NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r MUST MATCH THE PERIOD

=$500*(F|A 5%,14)∞+$100*(P|G 5%,14)∞*(F|P 5%,14)∞

=$500*(P|A 5%,14)∞+$100*(P|G 5%,14)∞

=$21,144.77*(P|F 5%,14)∞

=$21,144.77*(A|F 5%,14)∞

A B C D E F G H12

456789

24252627282930313233343536373839404142434445464748

PROBLEM 2.178

r= 5.00% PER 6 MONTHSc= 20.00% PER 6 MONTHSn= 14 6 MONTH PERIODSA= $500.00 PER 6 MONTHS

a F= $42,410.96

=500*(EXP(5%*14)-EXP(20%*14))/(EXP(5%)-EXP(20%))

b P= $21,060.66

=500*(1-EXP((20%-5%)*14))/(EXP(5%)-EXP(20%))P= $21,060.86 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS

c A= $2,145.15 USING CONTINUOUS COMPOUNDING INTEREST TABLES THIS IS

TABLE TO ILLUSTRATE AND CHECK ANSWER TO a AND b

PERIOD PYT FW PW01 $500.00 $957.77 $475.612 $610.70 $1,112.77 $552.593 $745.91 $1,292.85 $642.014 $911.06 $1,502.08 $745.915 $1,112.77 $1,745.17 $866.636 $1,359.14 $2,027.60 $1,006.887 $1,660.06 $2,355.74 $1,169.828 $2,027.60 $2,736.97 $1,359.149 $2,476.52 $3,179.91 $1,579.10

10 $3,024.82 $3,694.53 $1,834.6511 $3,694.53 $4,292.43 $2,131.5612 $4,512.51 $4,987.09 $2,476.5213 $5,511.59 $5,794.17 $2,877.3014 $6,731.87 $6,731.87 $3,342.95

14 =500*EXP(20%*(14-1))14 =6731.87*EXP(5%*(14-14))14 =6731.87*EXP(-5%*14)

SUM $42,410.96 $21,060.66

NOTE! SINCE n IN THE FORMULAS AND TABLES IS THE NUMBER OF PAYMENT PERIODS, r AND c MUST MATCH THE PERIOD

NOTE! PAYMENTS ARE INCREASING AT A CONTINUOUSLY COMPOUNDED 20%, NOT JUST 20%.

=$42,410.96*(P|F 5%,14)∞

=$42,410.96*(A|F 5%,14)∞

A B C D E F G12

22232425262728293031323334353637383940414243444546

PROBLEM 2.179

r= 10.000% PER YEAR COMPOUNDED CONTINUOUSLYYRS= 7

= $1,000.00 PER YEAR CONTINUOUS FLOW

a F= $10,137.53

=1000*(EXP(10%*7)-1)/10%F= $10,137.53

=$1,000*(F| 10%,7)

b P= $5,034.15

=1000*((EXP(10%*7)-1)/(10%*EXP(10%*7)))P= $5,034.15

=$1,000*(P| 10%,7)

P= $5,034.20

USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST FORMULAS THIS IS

USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST TABLES THIS IS

=$10,137.53*(P|F 10%,7)∞

A B C D E F G H123456

PROBLEM 2.180

r= 10.000% PER YEARYRS= 7

P= $20,000.00

$3,972.87

=20000*10%*EXP(10%*7)/(EXP(10%*7)-1)

$3,972.80

=$20,000*( |P 10%,7)

USING CONTINUOUS COMPOUNDING CONTINUOUS FLOW INTEREST TABLES THIS ISA

A B C D E F G H123456

Chapter 2 - All 180 Problems!.xls

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