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# final value of PV

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Need help with the following problems. I would like see how to solve each problem with a formula and what inputs you would use when using a financial calculator.

1. Your parents are giving you \$500 a month for five years while you attend college to earn both a bachelor's and a master's degree. At a 7 percent discount rate, what are these payments worth to you when you first enter college?
2. You just won the lottery! As your prize you will receive \$1,500 a month for twenty years. If you can earn 9 percent on your money, what is this prize worth to you today?
3. Angela is able to pay \$230 a month for 6 years on a car loan. If the interest rate is 7.9 percent, how much can she afford to borrow to buy a car?
4. Your employer contributes \$50 a week to your retirement plan. Assume that you work for your employer for another 12 years and that the applicable discount rate is 8 percent. Given these assumptions, what is this employee benefit worth to you today?
5. You have a sub-contracting job with a local manufacturing firm. Your agreement calls for annual payments of \$82,000 for the next 3 years. At a discount rate of 9.5 percent, what is this job worth to you today?
6. Swenson & Swenson just decided to save \$2,200 a month for the next 6 years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 5.5 percent interest compounded monthly. They deposit the first \$2,200 today. If the company had wanted to deposit an equivalent lump sum today, how much would they have had to deposit?
7. You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of \$15 a month for the next nine months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 2 percent interest per month. How much money are you borrowing?
8. You are scheduled to receive annual payments of \$15,000 for each of the next 13 years. The discount rate is 9 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?
9. You are comparing two annuities with equal present values. The applicable discount rate is 11.25 percent. One annuity pays \$6,000 on the first day of each year for 25 years. How much does the second annuity pay each year for 25 years if it pays at the end of each year?

#### Solution Preview

1. Your parents are giving you \$500 a month for five years while you attend college to earn both a bachelor's and a master's degree. At a 7 percent discount rate, what are these payments worth to you when you first enter college?
r=7%/12
C=\$500
n=5*12=60
we need FV=C/r*((1+r)^n-1) = 500/(7%/12)*((1+7%/12)^60-1)=\$35,796.45

On your calculator do the following:
Clear the TVM worksheet, press 2ND and then CLR TVM
Enter number of payments type 60 and then press N
Enter interest rate type 7 and then press I/Y
For per month payments type 500 and then press PMT
To set that the payments are monthly press 2ND, P/Y and type 12 press ENTER
To get the final value of FV, press CPT and FV. You will get the answer.

2. You just won the lottery! As your prize you will receive \$1,500 a month for twenty years. If you can earn 9 percent on your money, what is this prize worth to you today?

r=9%/12
C=\$1500
n=20*12=240
we need PV=C/r*(1-1/(1+r)^n) = 1500/(9%/12)*(1-1/(1+9%/12)^240)=\$166,717.43

On your calculator do the following:
Clear the TVM worksheet, press 2ND and then CLR TVM
Enter number of payments type 240 and then press N
Enter interest rate type 9 and then press I/Y
For per month payments type 1500 and then press PMT
To set that the payments are monthly press 2ND, P/Y and type 12 press ENTER
To get the final value of PV, press CPT and PV. You will get the answer.

3. Angela is able to pay \$230 a month for 6 years on a car loan. If the interest rate is 7.9 percent, how much can she afford to borrow to buy a car?
r=7.9%/12
C=\$230
n=6*12=72
we need PV=C/r*(1-1/(1+r)^n) = 230/(7.9%/12)*(1-1/(1+7.9%/12)^72)=\$13154.54

On your calculator do the following:
Clear the TVM worksheet, press 2ND and then CLR TVM
Enter number of payments type 72 and then press N
Enter interest rate type 7.9 and then press I/Y
For per month payments type 230 and then press PMT
To set that the payments are monthly press ...

#### Solution Summary

The final value of PV is determined.

\$2.19
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