PART 1: Setup.

Math 1090 Project

Present Value

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(Work in groups of two to four.)

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This schedule shows a record of payments, interest paid, and a running balance. This schedule also allows for extra payments to be made, and it keeps track of the amount of principle being paid. The fixed values at the beginning of the spreadsheet are: the amount of the loan (formatted as "currency" in cell C2), the annual interest rate (APR formatted as "percentage" with at least 3 decimal places in cell C3), the time for the loan (in cell E2), and the number of payments per year (in cell E3). The minimum payment to complete the loan according to its program is figured in cell C5 from these values using an amortization formula like the one at the bottom of page 345 in the text College Algebra in Context by

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=C2*C3/E3/(1-(l+C3/E3)A-(E2*E3)) an ~formatted as "currency."

A B c D E F 1 LOAN PAYMENTS 2 Loan Amount Time (years) 3 Interest Rate Payments per Year

4 5 Payment Amount I

6 Payment Reg. Payment Extra Pay Interest Principle Paid Balance remaining

7 8 9

It is good to start the schedule before the first payment, so enter a zero in cell A 7, and in cell F7 enter =C2, the amount to pay at the begir ~ng of the loan. In cell A8 and enter the formula = l +A7. In cell B8, enter =$C$5; rememl er the $' s keep this reference to this cell as the formula is copied down, so be sure to include the :n. In cell C8 enter =C7 to copy whatever the previous amount is. In cell D8 enter =$C$3*F7 /$E$3 (the APR x bal~ce +number of payments per

year) so that all the formulas copies from here will continue to refer to the interest rate in C3 divided by the number of payments per year times the amount in the account at the end of the previous month- in cell F7 now. In cell E8 enter =B8- D8 (the$ payment - $ interest). Finally, in cell F8 enter =F7-C8- E8 (the previous balance - extra payment - principle paid), and format cells B7 to F8 as "currency."

Example: To check if the formulas are clrrect, enter 232000 in C2, 0.05375 in C3, 20 in E2, and 12 in E3. Your spreadsheet should ni w look like the following:

A B c D E F 1 LOAN PAYMENTS 2 Loan Amount $323,00~.00 Time (years) 20 3 Interest Rate 5.3i 5% Payments per Year 12 4 I

5 Payment Amount $1,579.56 6 Payment Reg. Payment Extra Pay futerest Principle Paid Balance remaining

7 0 -- -- -- -- $232,000.00 8 1 $1,579.56 0.00 $1,039.17 $540.40 $231 ,459.60 9

When all the formulas are correct, highlight cells A8:F8, select Copy from the gdit menu, then highlight cells A9:F247, and use the Enter key to see all240 payments.

PART 2: Assignment

la. Adapt this spreadsheet to develop an amortization schedule for a 4-year car loan if $16,700 is borrowed at 8.2%, compounded monthly. Enter 16700 in cell C2, 0.082 in cell C3, and 4 in cell E2. 1

b. Using the spreadsheet above, row 55 shows the 48th payment, so in cell A56 enter the word TOTAL, in cell B56 hit the summation icon E in the menu bar at the top of the spreadsheet to find the total amount paid from B8:B55. Also enter the total amount of interest paid in cell D56, and the total amount of principle paid in cell E56. (The remaining balance after making the last payment should be zero, and there is no total for the remaining balances.)

c. Adjust the page margins and print the complete spreadsheet on one page.

d. Write a few sentences explaining what you observed in constructing your spreadsheet for this loan schedule. I

2a. Adapt your spreadsheet to develop j amortization schedule for a 10-year mortgage loan, of $80,000 at 7.2%, compounded monthly. There is no extra payment in this problem, so that column has not been included. Do nf print the whole schedule. Only write the amounts of each payment, interest paid, pr· ciple paid, and remaining principle for the 1st, the 60th, the last payments, plus the to s, in the table below. 2

Payment Interest Principle Paid

b. Change the number of payments per year to 24, divide the amount of each payment in half, and look at twice the total number of payments so that the spreadsheet approximates how the loan would be repaid if it was paid back semimonthly. Use this new spreadsheet to

write the amounts of interest paid, pf inciple paid, and remaining principle for only the 15

\ the 60th, the 120th, the 180th, the I st payments, plus the totals.

Payment Reg. Payment futerest Principle Paid Balance remaining 1 l ~ ~ - "D't

.,. ... t{D J.J.~. 6Cf ('\ , 771 -~} c;

60 l.' L <t>. ott l e: :S. q 1 ") 7."). \ 1! GSO~-.t~ 120 ~ ('8 ~ 0'\ 1 r,j :J_ .. s ";)_ 5~S · 7 ') <{ 71 l ~ . 2JD 180 l-lb~ - 01 lf5 . \ 7 s 'bttA. ~ '.)_:;;£ b7.t~ 240 t.\~ .04 ~ ~ " Lj{) t{ ' " • b_'{ $0.00 total \ t "J._ $£{ ' . ~() 31 '3~ \ ~Q ~()C) .<10 --

c. Write a few sentences explaining what you observed, including the total interest paid, when payments are made twice a month instead of once a month.

3a. A recent college graduate brought a n4w car by borrowing $18,000 at 8.4%, compounded monthly, for five years. Adapt your spreadsheet to make the amortization schedule and use it to fill in the table below. 3

Loan Amount $18,000.00 Time (years) 5 Interest Rate 8.4% Payments per Year 12

I Payment Amount '36 g -L-1 ~

Payment Reg. Payment Extra Pay Interest Principle Paid Balance remaining 0 -- -- -- -- $18,000.00 1 '>b 1S • Lj'3 $0.00 l'l-' ..... ·~ ~}_ .. ll ~ 1//S 7 -s·?

15 )(.., 7J . L\~ $0.00 I o 1- \ ~ .2f>7-3D Jl(J 17 c'/.., '6'? 30 -.f~ ~ .l.l) $0.00 ;~.<:.S ~~b .. 71 1'{]!,,. cl_"'( 60 -~f? -i3 $0.00 2 -s"' 3'S. '87 $0.00

total ~u .. "\ ~ $0.00 q ib'S .. 8 .. , ~~600""" ~.:2 l 6 5 ~~'"'1

b. Enter "15" in cell C8 to investigate ho ~ a $15 extra payment will effect repaying the loan .. Note: The remaining balance goes to ~ero before sixty payments are made. Identify which number payment that occurs. Be sure to add the total "extra payments" at the bottom of column C to the total amount paid at t ~e bottom of column B. Fill in the amounts of interest paid, principle paid, and re ~mining principle for the 18

\ 15th, 301h, and the last payment for the schedules with the xtra principle paid.

Loan Amount $18,000.(0 Time (years) 5 Interest Rate 8.4 ~ Payments per Year 12

Payment Amount ~~[S~>Lf1 Payment Reg. Payment Extra Pay futerest Principle Paid Balance remaining

0 -- -- -- -- $18,000.00 1 ""%~- tl? $15.00 1').(;;,"" ';),_<-/ <. '~ ~5 17?'-1~ .5,>

15 sro'6 . c.{~ $15.00 1'1 -S1 ;;)_'~ ~'6'1 I~ 4'-f"f. ~ 7 30 )bC6. 13 $15.00 I GfS,;).g ~60~ i ~ 4"/"Sq.LI1>

(last number) ..l.i.-::o ~ ~~ , ~~ .. c ~ $? I .. ~I ~s-71 $0.00 total $? I --

c. Write a few sentences explaining what you observed, including the total interest paid, when payments are made twice a month instead of once a month.

4a. A young couple buying their first home borrows $85,000 for thirty years at 7.2%, compounded monthly. Write the amounts of interest paid, principle paid, and remaining principle for the 15

\ the lih, the 60th, and the last payment. 4

Payment 0 1

12 60 120 240 360 total

Loan Amount Interest Rate

Payment Amount Reg. Payment

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$85,000.00 Time (years) 7.2% Payments per Year

Extra Pay Interest

$0.00 510 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

30 12

Principle Paid Balance remaining $18,000.00 ~So 0 0

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$0.00

b. Suppose they make the required payment for the first twelve months. However, with the twelfth payment only, they are also aJle to pay an extra $1000. Print the adjusted schedule and answer how many payments, and how much money, will they save because of this single extra payment? (Note: The ext a $1000 is made on the 12th payment only, and be sure to add the extra payment to the t::>tal paid.)

Loan Amount $85,000.( I() Time (years) 30 Interest Rate 7.27lo Payments per Year 12

Payment Amount Payment Reg. Payment Extra Pay Interest Principle Paid Balance remaining

0 -- -- -- -- $18,000.00 1 1?t Jl7 $0.00 f:i,lD 6b -cf.7 <t_ Lj tt ) ~ .,0 "\

12 S 7G . tt I $0.00 I 5oS . qu\ 71., "S 5 ~3/CC(.~cl

13 S76 · q7 $1000.00 ~t{i\41 ,0~ 7)- qs. 2!3Lbtlt·~ 60 .:::; 7 b . 0.? $0.00 q .73 '1\ 103 -~" 78 <gl.J) ,C/f 120 S 7G .Cif. 7 $0.00 <-{~1.1~ 147.95 713 7d..·0'1 240 S 7G · t( / $0.00 ~73. "J CJ,7 '>a:S .., lO 4S54d..4g

(last number) -~.:ss. .. \to $0.00 ;2,d 35/ .. bS $0.00 total ~00 1'A4~77 $1000.00 \ IS ~gt-{ ~000 --

c. Write a few sentences explaining what you observed, including the total interest paid, compared to what the total interest would have been without the extra payments. Make the comparison in both absolute terms ($'s) and relative terms(% difference).

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Part III: Reflection

Did this project change the way you think about buying a home or a car? Write one paragraph stating what ideas changed and why. If this project did not change the way you think, write how this project gave further evidence to support your existing opinion about buying a home or a car. Be specific.

1 Based on problem #35, page 483, Harshbarger & Reynolds, Mathematical Applications, 7th ed. 2 Based on problem #36, page 483, Harshbarger & Reynolds, Mathematical Applications, 7th ed. 3 Based on problem #37, page 483, Harshbarger & Reynolds, Mathematical Applications, 7th ed. 4 Based on problem #38, page 483, Harshbarger & Reynolds, Mathematical Applications, 7th ed.

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LOAN PAYMENTS ('/ CA f "'-( ff_ ~ 0 h "- t;;"A.-Loan Amount 16700 Time(years) 4 .:> "L.v- '-"-e l e fer'!:!t.-Interest Rate 8.20% Payments/yr 12

Payment Amount $409.27 Payment Reg. Payment Extra Pay Interest Principle Paid Balance Remaining loo~L 0 $16,700.00

1 $409.27 $114.12 $295.15 $16,404.85 2 $409.27 $112.10 $297.17 $16,107.69 3 $409.27 $110.07 $299.20 $15,808.49 4 $409.27 $108.02 $301.24 $15,507.25 5 $409.27 $105.97 $303.30 $15,203.95 6 $409.27 $103.89 $305.37 $14,898.58 7 $409.27 $101.81 $307.46 $14,591 .12 8 $409.27 $99.71 $309.56 $14,281 .56 9 $409.27 $97.59 $311 .67 $13,969.88

10 $409.27 $95.46 $313.80 $13,656.08 11 $409.27 $93.32 $315.95 $13,340.13 12 $409.27 $91 .16 $318.11 $13,022.02 13 $409.27 $88.98 $320.28 $12,701.74 14 $409.27 $86.80 $322.47 $12,379.27 15 $409.27 $84.59 $324.67 $12,054.60 16 $409.27 $82.37 $326.89 $11 ,727.71 17 $409.27 $80.14 $329.13 $11 ,398.58 18 $409.27 $77.89 $331.38 $11 ,067.20 19 $409.27 $75.63 $333.64 $10,733.57 20 $409.27 $73.35 $335.92 $10,397.65 21 $409.27 $71 .05 $338.21 $10,059.43 22 $409.27 $68.74 $340.53 $9,718.90 23 $409.27 $66.41 $342.85 $9,376.05 24 $409.27 $64.07 $345.20 $9,030.86 25 $409.27 $61 .71 $347.55 $8,683.30 26 $409.27 $59.34 $349.93 $8,333.37 27 $409.27 $56.94 $352.32 $7,981 .05 28 $409.27 $54.54 $354.73 $7,626.32 29 $409.27 $52.1 1 $357.15 $7,269.17 30 $409.27 $49.67 $359.59 $6,909.58 31 $409.27 $47.22 $362.05 $6,547.53 32 $409.27 $44.74 $364.52 $6,183.00 33 $409.27 $42.25 $367.01 $5,815.99 34 $409.27 $39.74 $369.52 $5,446.47 35 $409.27 $37.22 $372.05 $5,074.42 36 $409.27 $34.68 $374.59 $4,699.83 37 $409.27 $32.12 $377.15 $4,322.68 38 $409.27 $29.54 $379.73 $3,942.95 39 $409.27 $26.94 $382.32 $3,560.63 40 $409.27 $24.33 $384.93 $3,1 75.69 41 $409.27 $21.70 $387.56 $2,788.13 42 $409.27 $19.05 $390.21 $2,397.92 43 $409.27 $16.39 $392.88 $2,005.04 44 $409.27 $13.70 $395.56 $1 ,609.47 45 $409.27 $11 .00 $398.27 $1 ,211 .21 46 $409.27 $8.28 $400.99 $810.22 47 $409.27 $5.54 $403.73 $406.49 48 $409.27 $2.78 $406.49 -$0.00

$19,644.74 $2,944.74 $16,700.00

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2 - 1 d - I noticed that when you begin making payments on the car, most of your money is going towards the interest. As you continue to make payments, more and more of your payment goes towards the principle until the car is paid off.

2 - 2c I noticed that when you make payments twice as often, you pay a bit less interest over the course of the loan. Over 10 years. you would save about $115

2 - 4c I noticed thaf when you make a single extra payment of $1000, it has a significant effect on how much interest you end up paying. Just that one payment will end up saving you almost $7000 over the course of the loan. You also end up paying off the loan sooner.

3- I think this project changed my opinion about making extra payments. I was fairly familiar with the way compound interest works and the whole process of amortizing a loan over time. I was very surprised to see the effect that making even a single extra payment can have on the loan over time.