Chapter 1 Homework - Purdue Universityjbeckley/q/WD/MA373/S15/S15 373... · Chapter 1 Homework 1. 2004 ... Principal is the ... Aric invested 1000 in a bank that pays compound interest

February 25, 2015 Copyright Jeffrey Beckley 2015

Chapter 1 Homework

1. 2004 + 2008 + … + 3300 =

( )(# )2

2004 3300( )(325) 861,900

2

Firstterm Lasttermterms

2. 5 + 25 + 125 + . . . + 78,125 =

First term – Next term after last

1 – ratio

85 5

97,6551 5

3. 1 + 0.8 + 0.82 + . . . 0.813 =

141 .8

4.78011 .8

4. If 5(1 ) 1.12,i calculate 5 10 1001 (1 ) (1 ) ... (1 ) .i i i

Geometric series, ratio is (1+i)5 or 1.12 100 20

21

(1 ) (1.12)

1 (1.12)81.69874

1 1.12

i


5. Hannah invests 2500 in a fund. At the end of 2.5 years, Hannah has 3000.

a. Calculate Hannah’s principal?

b. Calculate the amount of interest that Hannah earned.

c. Calculate (0).A

d. Calculate (2.5).A

e. Determine (2.5).a

a) Principal is the original amount of the loan, so K=2,500

b) Interest = S(the accumulated value) – K(the principal) = 3,000 - 2,500= 500

c) A(0) = K = 2,500

d) A(2.5) = accumulated value after 2.5 years = 3,000

e) a(2.5) = accumulation function = A(2.5)/A(0) = 3000/2500 = 1.2

6. Jake invests X in a Fund with an accumulation function of 2( ) 1 0.02 0.01a t t t . At the end

of six years, Jake has 29,600.

a. Calculate X . 2(6) 1 (.02)(6) (.01)(6) 1.48

(6) (1.48) 29,600

20,000

a

Xa X

X

b. Calculate the amount interest earned by Jake.

Amount of interest = 29,600-20,000=9,600

c. Calculate [2,3.5]i .

[2,3.5]

2

2

(3.5) (2) 1.1925 1.080.1041667

(2) 1.08

(3.5) 1 0.02(3.5) 0.01(3.5) 1.1925

(2) 1 0.02(2) 0.01(2) 1.08

a ai

a

a

a


7. Sam invests 1000 in a fund with an accumulation function of 3( )a t t . At the end of two

years, Sam has 1200.

a. Determine and . 2

3

(0) 1 (0) 1 1

1000 (2) 1200 1000(1 (2) ) 1200 1 8 1.2 .025

a

a

b. Determine the amount that Sam will after 4 years. 31000 (4) 1000(1 0.25(4) ) 2600a

c. Determine the amount of time necessary for Sam’s money to double. 3

3

1000(1 0.025 ) 2000

40

3.41995

t

t

t

8. Xinyuan invests 3000 in an investment that has an accumulation function of 2t t . At

the end of 3 years, Xinyuan has 3162. At the end of 5 years, Xinyuan has 3330.

Determine how much Xinyuan will have at the end of 10 years. 2(0) 1 (0) (0) 1 1

3000 (3) 3000(1 3 9 ) 3162 1 3 9 1.054 3 9 0.054

3000 (5) 3000(1 5 25 ) 3330 1 5 25 1.11 5 25 0.11

(3 9 .054)* 5

(5 25 .11)*3

Add the two equations above

a

a

a

2

to get 30 0.06 .002

1 3 9(.002) 1.054 .012

3000 (10) 3000(1 (.012)(10) (.002)(10 )) 3960a


9. Joon invests in an account with an accumulation function of 2( ) 1 0.028 0.001a t t t .

Calculate:

a. [1,3]i

(3) (1) 1 .028(3) .001(9) [1 .028(1) .001(1)] 1.093 1.029.0621963

(1) 1 .028(1) .001(1) 1.029

a a

a

b. The amount of interest that Joon will earn from time 1 until time 3 assuming he invests

2000 now

2000 (3) 2000 (1) 2000(1.093) 2000(1.029) 128a a

c. [2,3]i

[2,3]

(3) (2). We know from above that a(3)=1.093

(2)

(2) 1 .028(2) .001(4) 1.06

1.093 1.06.0311321

1.06

a ai

a

a

d. 3 [2,3] 0.0311321i i

e. The annual effective interest rate during the third year. 3 [2,3] 0.0311321i i

f. [2.5,3.2]i

2

2

[2.5,3.2]

(3.2) (2.5)

(2.5)

(3.2) 1 .028(3.2) .001(3.2) 1.09984

(2.5) 1 .028(2.5) .001(2.5) 1.07625

1.09984 1.07625.0021918699

1.07625

a a

a

a

a

i

10. You are given that:

a. (3) 1.166424a

b. 1 0.05i

c. 2 0.06i

Calculate 3i .


3

(1) (0) (1) 10.05 (1) 1.05

(0) 1

(2) (1) (2) 1.050.06 (2) 1.113

(1) 1.05

(3) (2) 1.166424 1.1130.048

(2) 1.113

a a aa

a

a a aa

a

a ai

a

11. Izzat invests 2500 in an account that pays simple interest at an annual rate of 5.6%.

a. Determine ( ).a t

a(t)=1+0.056t

b. Determine ( ).A t

A(t)=2500(1+0.056t)

c. How much will be in the fund at the end of 8 years?

2500(1+0.056(8))=3620

d. How much interest will Izzat earn during the first year?

2500(1+0.056)-2500=140

e. How much interest will Izzat earn during the eighth year?

2500(1+0.056(8))-2500(1+0.056(7))=140

f. Calculate 1i .

1

0.056.056

1 ( 1) 1 0(0.056)

ii

n i

g. Calculate 5i .

5

0.056.0457516

1 ( 1) 1 4(0.056)

ii

n i

12. Hannah invests 2500 in a fund which pays simple interest. At the end of 2.5 years, Hannah has

3000.

a. Determine .s

b. If Hannah had invested 12,000, how much would she have after 6 years?

a)

30001

25002500(1 2.5 ) 3000 0.082.5

s s

b) 12000(1 0.08(6)) 17760


13. Peilun invests 10,000 at a simple interest rate of 5%. At the end of n years, Peilun has 17,000.

Determine .n

10000(1 .05 ) 17000 1 .05 1.7 .05 0.7 14n n n n

14. Jason invests Y in a fund earning a simple interest rate of 7%. At the end of 9 years, Jason has

743.28.

Determine .Y

Y(1 9(.07)) 1.63 743.28 456Y Y

15. Yichu invests 100,000 in an account that pays simple interest. The annual effective interest rate

earned by Yichu in the 26th year is 2%.

Determine how much money Yichu will have at the end of the 26th year.

26

(26) (25) 1 26 (1 25 )0.02 0.02 0.5 0.04

(25) 1 25

100,000(1 .04(26)) 204,000

a a s si s s s

a s

16. Izzat invests 2500 in an account that pays compound interest at an annual rate of 5.6%.

a. Determine ( ).a t

( ) (1.056)ta t

b. Determine ( ).A t

( ) 2500(1.056)tA t

c. How much will be in the fund at the end of 8 years? 82500(1.056) 3865.91

d. How much interest will Izzat earn during the first year?

2500(1.056)-2500=140

e. How much interest will Izzat earn during the eighth year?

2500(1.056)8-2500(1.056)7=205.01

f. Calculate 1i .

1

(1) (0) 1.056 10.056

(0) 1

a ai

a

g. Calculate 5i .

5 4

5 4

(5) (4) (1.056) (1.056)0.056

(4) (1.056)

a ai

a


17. Hannah invests 2500 in a fund which pays compound interest. At the end of 2.5 years, Hannah

has 3000.

a. Determine .i 2.5 2.5

1/2.5

2500(1 ) 3000 (1 ) 1.2

1 (1.2) 1.0756538 7.56538%

i i

i i

b. If Hannah had invested 12,000, how much would she have after 6 years? 612,000(1 0.0756538) 18587.30

18. Fei lends Dris 1450 today. Dris agrees to repay the loan at the end of three years based on

compound interest at an annual effective interest rate of 10%.

Determine the amount that Dris will repay. 31450(1.10) 1929.95

19. Michaela needs to have 25,000 at the end of 5 years to buy a car. She has the option of

investing in two Funds. Fund A pays a simple interest rate of 5.5% while Fund B pays compound

interest at a rate of 5%.

a. If Michaela invests in Fund A, how much would she need to invest in order to have

25,000 at the end of 5 years?

X(1 0.055*5) 25,000 19,607.84X

b. If Michaela invests in Fund B, how much would she need to invest in order to have

25,000 at the end of 5 years? 5(1.05) 25,000 19,588.15X X

c. Which account should Michaela invest in and why?

Michaela should invest in Fund B because she will invest less money than Fund A and

still get the same accumulated amount.


20. Max borrows 2000 from Lisa. He agrees to repay the loan at the end of 5 years with a payment

of 4000.

Determine the compound annual interest rate earned by Lisa on this loan. 5 52000(1 ) 4000 (1 ) 2 14.86984%i i i

21. Aric invested 1000 in a bank that pays compound interest at an annual effective rate of 9.25%.

Aric now has 5000.

Determine the number of years that have passed since Aric invested the money.

1000(1 0.0925) 5000 1.0925 5

*ln(1.0925) ln(5) 18.19218

t t

t t

22. Mengyun invests 1275 in a fund that pays compound interest for 11 years.

The interest rates are:

i. 5.5% for the first four years;

ii. 6.5% for the next 5 years; and

iii. 3% for the last 2 years.

Determine the amount Mengyun will have after 11 years.

Determine the level annual effective interest rate that is equivalent to the rates that Mengyun

earned. 4 5 2

11 11

1/11

1275(1.055) (1.065) (1.03) 2295.844723

1275(1 ) 2295.844723 (1 ) 1.800662527

1.800662527 1

5.49239%

i i

i

i


23. Ryan invests 5,000 in an account earning simple interest of 4%.

Prateek invests X in an account earning 2% compounded annually.

In year Y, Prateek and Ryan earn the same annual effective interest rate.

At the end of year Y, the amount of money in Prateek’s account is equal to the amount of

money in Ryan’s account.

Determine X.

26

1 0.04 (1 0.04(Y 1))0.02 0.02 0.0008 0.0008 0.04 26

1 0.04(Y 1)

5000(1 0.04(26)) (1.02) 6095.31

YY Y

X X

24. Alex invests 100 in an account earning simple interest. During the 10th year, the amount of

interest that Alex earns is 20.

Charlene invests X into an account earning compound interest of .i During the 10th year, the

amount of interest that Charlene earns is also 20.

During the 11th year, Alex and Charlene earn the same annual effective interest rate.

Determine X .

Solution: Interest is the same in all years for simple interest.

Or (10) (9) 20 100(1 10 ) 100(1 9 ) 20 100 20 0.20A A s s s s

(11) (10) 1 11(0.2) (1 10(0.2))0.06667

(10) 1 10(0.2)compound

a ai

a

10 9(1.06667) (1.06667) 20 0.11917 20 167.827X X X X

100(1 ) 100 20 1 1.2 20%s s s


25. Sarah borrows 2700 to buy a piano. The loan will be repaid in one year and requires interest in

advance. The discount rate is 8%.

a. Determine the amount of principal in the loan.

Principle = amount paid up front = K = 2700

b. Determine the amount of money Sarah will have at time 0 to spend on a piano.

K-K*D=2700-2700(.08)=2484

c. Determine the amount of money that Sarah will need to repay after one year.

2700

d. Calculate the amount of discount that Sarah will pay.

Discount = K*D = 2700(.08)=216

26. Joon invests in an account with an accumulation function of 2( ) 1 0.028 0.001a t t t .

Calculate:

a. [1,3]d

2 2

[1,3] 2

(3) (1) (1 0.028(3) 0.001(3 )) (1 0.028(1) 0.001(1 )).0585544

(3) 1 0.028(3) 0.001(3 )

a ad

a

b. [2,3]d

2 2

[2,3] 2

(3) (2) (1 0.028(3) 0.001(3 )) (1 0.028(2) 0.001(2 )).0301921

(3) 1 0.028(3) 0.001(3 )

a ad

a

c. 3d

2 2

3 [2,3] 2

(3) (2) (1 0.028(3) 0.001(3 )) (1 0.028(2) 0.001(2 )).0301921

(3) 1 0.028(3) 0.001(3 )

a ad d

a

d. The annual effective discount rate during the third year.

3 [2,3]

2 2

2

(3) (2)Annual effective discount =

(3)

(1 0.028(3) 0.001(3 )) (1 0.028(2) 0.001(2 )).0301921

1 0.028(3) 0.001(3 )

a ad d

a

e. [2.5,3.2]d

2 2

[2.5,3.2] 2

(3.2) (2.5) (1 0.028(3.2) 0.001(3.2 )) (1 0.028(2.5) 0.001(2.5 )).0214486

(3.2) 1 0.028(3.2) 0.001(3.2 )

a ad

a


27. You are given that 5 0.06d . Calculate 5i .

55

5

.06.0638298

1 .94

di

d

28. You are given that 5 0.08i . Calculate 5d .

55

5

.08.0740741

1 1.08

id

i

29. You are given that 2( ) 1 0.03a t t .

a. Determine ( ).v t

2

1 1( )

( ) 1 0.03v t

a t t

b. Calculate (3.5).v

2

1 1(3.5) 0.73126

(3.5) 1 0.03(3.5 )v

a

c. Tracy wants to have 1000 at the end of 5 years. How much must she invest today to

achieve her goal.

2

* (5) 1000 1000 (5)

1(5) 0.571428571

1 0.03(5 )

571.43

X a X v

v

X

30. Shivam wants to buy a car in 5 years for 30,000. Today, he will invest X in an account earning

simple interest at 6% in order to have the 30,000 in five years.

Determine X .

(1 0.06(5)) 30,000

23,076.92

X

X

31. Shivam wants to buy a car in 5 years for 30,000. Today, he will invest X in an account earning

compound interest at 6% in order to have the 30,000 in five years.

Determine X . 5(1.06) 30000

22,417.75

x

x


32. Calculate the present value of 100,000 to be paid 8 years from today using a compound annual

effective interest rate of 6.7%. 8(1.067) 100,000

59,522.98

X

X

33. The present value of 26,700 to be paid at the end of 6 years is 20,000.

Calculate the annual effective interest rate. 6 6

1/6

20,000(1 ) 26,700 (1 ) 1.335

1.335 1 0.0493335

i i

i i

34. You are given that 1

( )( )

v tt

.

Using this discount function, a payment of 200 to be made at time 10 has a present value of 100

at time 0.

Calculate (20).a

1 1(0) 1 1 1 1

(0)

200 (10) 100

1200( ) 100

(10)

200100 200 100 100 .1

10 1

1 1( ) ( ) .1 1

.1 1 ( )

(20) .1(20) 1 3

v

v

v t a t tt v t

a


35. Shi Corporation is building a new factory. Shi expects the factory will generate the following

cash flows:

Time Cash Flow

0 - 500,000

1 - 100,000

2 200,000

3 300,000

4 400,000

5 100,000

a. Calculate the Net Present Value at an annual effective interest rate of 10%.

0

1

2

3

4

5

500,000

100,000

200,000

300,000

400,000

100,000

10

135,072.12

C

C

C

C

C

C

I

NPVCPT

b. Calculate the Net Present Value at an annual effective interest rate of 20%.

0

1

2

3

4

5

500,000

100,000

200,000

300,000

400,000

100,000

20

37,744.34

C

C

C

C

C

C

I

NPVCPT

c. Calculate the Internal Rate of Return (IRR).

0

1

2

3

4

5

500,000

100,000

300,000

400,000

300,000

100,000

17.44745%

C

C

C

C

C

C

IRRCPT


d. What is the Net Present Value at the IRR. (Note: You should be able to answer this

question without doing any work.)

0 because IRR is the interest rate at which NPV = 0

36. Jiang Corporation invests X million today to build a factory. The factory is expected to produce

the following profits:

End of Year Profits

1 1 million

2 4 million

3 2 million

4 1 million

At the end of 4 years, the factory will be obsolete and will be closed.

The Net Present Value of this project to Fisher Corporation is 1 million at an interest rate of 7%.

Calculate the Internal Rate of Return on this project.

2 3 4

0

1

2

3

4

1 1 1 11( ) 4( ) 2( ) 1( ) 1 million

1.07 1.07 1.07 1.07

5.823825 million

5.823825

1

4

2

1

14.62703%

X

X

C

C

C

C

C

IRRCPT


37. Noah borrows 26,000 to be repaid at the end of 5 years. The loan charges an annual compound

discount rate of 5.8%.

a. Determine ( )a t .

1 1 1( ) (0.942)

(1 ) (1 0.058) (0.942)

t

t t ta t

d

b. Calculate the amount of cash that Noah will receive from this loan at time 0. 526,000(1 0.058) 19,285.36

c. Calculate the amount that Noah will have to repay at the end of 5 years.

26,000

d. Calculate the amount of discount that Noah will pay.

26,000-19,285.36=6714.64

38. Kristen has a choice of two loans. Loan A charges an annual effective interest rate of 8%. Loan

B charges an annual effective discount rate of 7.4%.

Which loan should Kristen take and why?

0.0740.0799136

1 1 0.074

di

d

She should take Loan B because the annual effective interest rate is lower, which is what you’re

looking for when taking out a loan.

39. Cassidy takes out a seven year loan with a compound annual effective discount rate. Under this

loan, Cassidy will receive 22,000 today and repay 29,000 at the end of seven years.

Determine the annual effective discount rate being paid by Cassidy. 7

7

22,000(1 ) 29,000

(1 ) 1.318181818

1 .961303822 3.86962%

d

d

d d

40. Rui invests 12,500 today. The fund credits interest at a rate that is equivalent to a compound

annual discount rate of 6.4%.

Calculate the amount that Rui will have in the account at the end of 6.5 years.

6.5

.064.068376068

1 0.936

12,500(1.068376068) 19,213.97

di

d


41. Daiana invests 12,300 in an account that earns a nominal annual interest rate of 6%

compounded quarterly.

How much will Daiana have after 5 years?

4*5.0612,300(1 ) 16,566.32

4

42. Sammie takes out a loan of 26,000 to pay for the cost of her education this year. At the end of

10 years, she must repay the loan. The loan charges a nominal annual rate of interest of 9%

compounded monthly.

Determine the amount that Sammie must repay at the end of 10 years.

12*100.0926,000(1 ) 63,735.28

12

43. You are given that (12) 0.12.i

a. Determine the equivalent monthly effective interest rate. (12) .12

0.0112 12

i

b. Determine the equivalent annual effective interest rate. (12)

12 12.12(1 i) (1 ) (1 ) 1.12682503

12 12

12.68250%

i

i

c. Determine the equivalent (4)i .

(4) (12)4 12

(4)4

(4) (4)

(4)

(1 ) (1 )4 12

(1 ) 1.126825034

1 1.030301 0.0303014 4

0.030301*4 0.121204

i i

i

i i

i

d. Determine the equivalent (2)d .

(2) (12)2 12

(2)1/2

(2)(2)

(1 ) (1 ) 1.126825032 12

(1 ) (1.12682503) 0.9420452352

0.057954765 0.057954765*2 0.11590952

d i

d

dd


44. Elijah takes out a 3 year loan of 20,000 with interest paid in advance. The nominal annual rate

of discount is 4% compounded quarterly.

a. Determine the amount of cash that Elijah will receive at the initiation of the loan.

3*40.04(1 ) 20,000 17,727.70

4X X

b. Determine the equivalent annual effective interest rate on Elijah’s loan.

40.04(1 ) 1.041020356 4.10204%

4i

45. Madi invests 100,000 at the bank. At the end of eight years, she has 189,245.72. Madi has

earned a nominal annual effective interest rate if (12)i compounded monthly during the eight

year period.

Determine (12)i .

(12)12*8

(12) (12)96 1/96

(12)

100,000(1 ) 189,245.7212

(1 ) 1.8924572 (1.8924572) 1 0.0066666712 12

0.0066666667*12 0.08

i

i i

i

46. Jiayi borrows 12,500 at an interest rate of 7% compounded quarterly. At the end of the loan,

Jiayi pays 21,035.00.

Calculate the length of Jiayi’s loan in years.

4*

4*

0.0712,500(1 ) 21,035.00

4

(1.0175) 1.6828

4 *ln(1.0175) ln(1.6828)

ln(1.6828)7.5

4ln(1.0175)

t

t

t

t


47. Anqi invest 10,000 today. Anqi earns the following interest or discount rates for the next eleven

years:

i. Quarterly effective rate of interest of 3% for the first three years;

ii. A nominal rate of interest of 9% compounded monthly during the fourth

through the sixth year;

iii. (4) 0.06d for the last five years.

Determine the value of Anqi’s investment at the end of eleven years.

12 3 4 53 4 .09 .06

10000 1.03 1 112 4

10000(1.425761)(1.3086454)(1.35293) 25,243.18

48. Chuyun invests 11,000 in an account that earns interest at a rate equivalent to a discount rate of 8% convertible semi-annually. How much will Chuyun have after 42 months.

(2)

(2) (12)2 12 2

(12)1/12

(12)42

0.08

0.08(1 ) (1 ) (1 ) 1.085069444

2 12 2

1.085069444 1 0.00682686312

11,000(1 ) 14,638.4112

d

d i

i

i

49. Bo wants to borrow money to buy a car.

Bank A offers Bo a loan with an annual effective interest rate of 8.0%. Bank B offers Bo a loan with an interest rate of 7.8% compounded monthly. Which loan should Bo select and state why. (Provide work to support your answer.)

(12)

(12)12 12

Bank A: 8%

Bank B: i 7.8%

0.078(1 ) (1 ) 1.08084981 (1 )

12 12

Bo should choose Bank A because it has a lower effective interest rate.

i

ii


50. Shivam invests 123,000 in an account that earns a nominal interest rate of 6% compounded

every 4 years.

a. Calculate the amount that Shivam will have at the end of 4 years.

(1/4)*40.06123,000(1 ) 152,520

1/ 4

b. Calculate the amount that Shivam will have at the end of 9 years.

(1/4)*90.06123,000(1 ) 199,573.973

1/ 4

51. Mikala invests 10,000 in an account earning a nominal interest rate of 6% convertible every two

years.

Matt’s friend Michaela invests K in an account earning a nominal rate of interest of 6%

convertible monthly.

After 10 years, the amount in Matt’s account is equal to the amount in Michaela’s account.

Determine K.

(1/2)*10 12*100.06 0.0610,000(1 ) (1 )

1/ 2 12

17623.41683 (1.819396734) 9686.41

K

K K

52. You are given that 0.08.i Calculate .

(1 ) ln(1 )

ln(1.08) 0.0769610

i e i

53. You are given that 0.10. Calculate .i

0.10(1 ) 1 0.1051709i e e

54. Ben invests 6500 in an account that credits 7% compounded continuously.

Calculate the amount that Ben will have at the end of 8 years. 0.07*86500 11,379.37e

55. Calculate the present value of 100,000 payable at the end of 20 years using an interest rate of

5% compounded continuously. 0.05*20 100,000 36,787.94Xe X


56. You are given that 2( ) 1 0.03a t t . Calculate 10 .

10 2

'( )

( )

0.06(10)0.15

1 0.03(10)

t

a t

a t

57. You are given that interest is credited using simple interest at a rate of 10%. You are also given

that 0.05t .

Determine t .

( ) 1 .10

'( ) .10

'(t) .10.05

(t) 1 .10(t)

0.05(1 0.10 ) 0.10 10

t

a t t

a t

a

a

t t

58. If 0.02t t , determine ( ).a t

20.02 0.01( )tdt ta t e e

59. Andrew invests 32,100 in an account today that pays 20.01t t .

How much will Andrew have in his account at the end of 6 years? 6

2

0

0.010.72

66 32

0 0

32,100 32,100 65,947.31

0.010.01 0.72

3

t

e e

tt


60. Josh invest 30,000 in an account at time 0 and an additional 6000 in the account at time 5.

If the account earns interest at 0.01 0.005t t where t is measured from time 0, calculate

the amount that Josh will have at the end of 10 years.

10 10

0 5

(0.01 0.05 ) (0.01 0.05 ).35 0.2375

102

0

102

5

30,000 6000 30,000 6000 50,180.48

0.0050.01 0.35

2

0.0050.01 0.2375

2

t dt t dt

e e e e

tt

tt

61. You are given 0.01 0.005t t where t is measured from time 0.

Determine the amount of money that must be invested at time 3 to have 8000 at time 7. 7

3

(0.01 0.005 )

77 2

3 3

.14

8000

0.005(0.01 0.005 ) 0.01 0.1925 0.0525 0.14

2

8000 6954.87

t dt

Xe

tt dt t

Xe X

62. Kehara invests 1000 in an account earning 0.02t t . At the end of t years, Kehara’s

investment has doubled.

Calculate t ( t will not be an integer.)

0

0.02

0

22

0

1000 2000

0.02 ln(2)

0.02ln(2) 0.01

2

ln(2) / 0.01 8.3255

t

t

t

t

e

t

tt

t


63. You are given:

a. 3( ) 1 0.001a t ct t where c is a constant

b. 10 0.14

Miao invests 1000 at time 0. How much will Miao have at time 10?

3

2

2

10 3

3

( ) 1 0.001

'( ) 0.003

'( ) 0.003(10)0.14

( ) 1 10 0.001(10)

(10 2)(0.14) 0.3

1.4 0.28 0.3 0.05

1000 (10) 1 0.05(10) 0.001(10) 2500

a t ct t

a t c t

a t c

a t c

c c

c c c

a

64. You are given that the nominal interest is 8% and the rate of inflation is 2.5%.

Calculate the inflation adjusted interest rate.

1+ j =1+ i

1+ r=

1.08

1.025= 1.0536585

j = 5.36585%

65. If the real interest rate is 6% and the rate of inflation is 3%, calculate the nominal interest rate.

1.06 =1+ i

1.03®1+ i = 1.0918

i = 9.18%

66. Chang has 100 and could use it to buy 80 songs from itunes. Instead, Chang invests his 100 at an

annual effective interest rate of 11.3% for 4 years. The price of songs on itunes is subject to an

annual effective rate of inflation of %r . At the end of 4 years, Chang can buy 101 songs.

Determine r .

4

4

4

100(1.113) 153.4548635 /101 songs

1.519355 / song =

100 / 80 1.25 / song =

1.25(1 ) 1.519355

(1 ) 1.215484

5%

now

before

r

r

r


67. A gallon of gasoline costs 3.00 today. Lewis has enough money to buy 100 gallons today. Instead of buying gasoline, Lewis decides to invest his money at an annual interest rate of 6.6%. If the annual rate of inflation over the next five years is 4.1%, calculate how many gallons of gasoline Lewis will be able to buy at the end of five years.

3(100) = $300

300(1.066)5 = 412.9593

3(1.041)5 = 3.66754

412.9593 / 3.66754 = 112.598


Answers

1. 861,900

2. 97,655

3. 4.78010

4. 81.69874

5.

a. 2500

b. 500

c. 2500

d. 3000

e. 1.2

6.

a. 20,000

b. 9600

c. 0.10417

7.

a. 1 and =0.025

b. 2600

c. 3.41995 years

8. 3960

9.

a. 6.21963%

b. 128.00

c. 3.11321%

d. 3.11321%

e. 3.11321%

f. 2.19187%

10. 4.8%

11.

a. 1 0.056t

b. 2500(1 0.056 )t

c. 3620

d. 140

e. 140

f. 5.6%

g. 4.57516%

12.

a. 8%

b. 17,760

13. 14

14. 456

15. 204,000


16.

a. (1.056)t

b. 2500(1.056)t

c. 3865.91

d. 140

e. 205.01

f. 5.6%

g. 5.6%

17.

a. 7.56538%

b. 18,587.30

18. 1929.95

19.

a. 19,607.84

b. 19,588.15

c. No Answer Given

20. 14.86984%

21. 18.19218 years

22. 2295.84 and 5.49239%

23. 6095.31

24. 167.83

25.

a. 2700

b. 2484

c. 2700

d. 216

26.

a. 5.85544%

b. 3.01921%

c. 3.01921%

d. 3.01921%

e. 2.14486%

27. 6.38298%

28. 7.40741%

29.

a. 2

1

1 0.03t

b. 0.73126

c. 571.43

30. 23,076.92

31. 22,417.75

32. 59,522.98

33. 4.93335%

34. 3


35.

a. 135,072.12

b. – 37,744.34

c. 17.44745%

d. 0

36. 14.62703%

37.

a. (0.942) t

b. 19,285.36

c. 26,000.00

d. 6,714.64

38. Answer not given.

39. 3.86962%

40. 19,213.97

41. 16,566.32

42. 63,735.28

43.

a. 1.00000%

b. 12.68250%

c. 12.1204%

d. 11.59095%

44.

a. 17,727.70

b. 4.10204%

45. 8%

46. 30 quarters = 7.5 years

47. 25,243.18

48. 14,638.41

49. No Answer Given

50.

a. 152,520

b. 199,573.97

51. 9686.41

52. 7.69610%

53. 10.51709%

54. 11,379.37

55. 36,787.94

56. 0.15

57. 10

58. 20.01te

59. 65,947.31

60. 50,180.48

61. 6954.87

62. 8.3255 years


63. 2500

64. 5.3659%

65. 9.18%

66. 5%

67. 112.598 gallons

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Chapter 1 Homework - Purdue Universityjbeckley/q/WD/MA373/S15/S15 373... · Chapter 1 Homework 1. 2004 ... Principal is the ... Aric invested 1000 in a bank that pays compound interest