Time Value of Money Extra Problem Set
Note: Your answers may be slightly off (i.e. up to $1) of the answers shown due to
differences in rounding as you work through the solution
1. You are planning to retire in twenty years. You'll live ten years after retirement. You want
to be able to draw out of your savings at the rate of $10,000 per year. How much would
you have to pay in equal annual deposits until retirement to meet your objectives?
Assume interest remains at 9%. [$1254]
2. You can deposit $4000 per year into an account that pays 12% interest. If you deposit
such amounts for 15 years and start drawing money out of the account in equal annual
installments, how much could you draw out each year for 20 years? [$19964.12]
3. What is the value of a $100 perpetuity if interest is 7%? [$1428.57]
4. If you get payments of $15,000 per year for the next ten years and interest is 4%, how
much would that stream of income be worth in present value terms? [$121663.50]
5. Your company must deposit equal annual beginning of year payments into a sinking fund
for an obligation of $800,000 which matures in 15 years. Assuming you can earn 4%
interest on the sinking fund, how much must the payments be? [$38415]
6. If you deposit $45,000 into an account earning 4% interest compounded quarterly, how
much would you have in 5 years? [$54908.55]
7. How much would you pay for an investment which will be worth $16,000 in three years?
Assume interest is 5%. [$13821]
8. You are considering the purchase of two different insurance annuities. Annuity A will pay
you $16,000 at the beginning of each year for 8 years. Annuity B will pay you $12,000 at
the end of each year for 12 years. Assuming your money is worth 7%, and each costs
you $75,000 today, which would you prefer? [$102228 and $95312]
9. If your company borrows $300,000 at 8% interest compounded semi-annually and agrees
to repay the loan in 10 equal semiannual payments to include principal plus interest, how
much would those payments be? [$36987.28]
10. How much should you be willing to pay for an RBC 5 of 2019 if similarly risky investments
yield 8%? [$825.22]
11. What is the appropriate price for a TDCT 4.5 of 2021 if the approximate yield to maturity
on similar bonds is 4%? [$1,040.88]
12. What is the cost of a car if you made a down payment of $3,000 today and signed a
lease for monthly payments of $450 and a residual of $12,000 with an APR of 6%?
13. How much will your lease payments be if you want to purchase a car with a sticker price
of $40,000 if you sign a lease with an APR of 4% and a residual of $16,000? [$593.25]
14. What will your monthly mortgage payments be if you buy a house for $250,000, make a
10% down payment, and negotiate a mortgage with an interest rate of 5% compounded
15. What will your monthly mortgage payments be if you buy a house for $320,000, make a
25% down payment, and negotiate a mortgage with an interest rate of 8% compounded
quarterly? [$1,839.66] Time Value of Money Extra Multiple Choice Practice Questions
THE ANSWERS TO THESE QUESTIONS HAVE NOT BEEN VERIFIED
1. The present value of a single future sum:
a. increases as the number of discount periods increases.
b. is generally larger than the future sum.
c. depends upon the number of discount periods.
d. increases as the discount rate increases
2. At 8 percent compounded annually, how long will it take $750 to double?
a. 6.5 years
b. 48 months
c. 9 years
d. 12 years
3. If the interest rate is zero:
a. PV = FV n
b. PV = FV
c. FV = PV
d. FV = PV/e n
4. You wish to borrow $2,000 to be repaid in 12 monthly installments of $189.12. The annual
interest rate is:
a. 24 percent.
b. 8 percent.
c. 18 percent.
d. 12 percent.
5. If you have $20,000 in an account earning 8 percent annually, what constant amount could
you withdraw each year and have nothing remaining at the end of 5 years?
6. You just purchased a parcel of land for $10,000. If you expect a 12 percent annual rate of
return on your investment, how much will you sell the land for in 10 years?
7. A commercial bank will loan you $7,500 for two years to buy a car. The loan must be
repaid in 24 equal monthly payments. The annual interest rate on the loan is 12 percent of
the unpaid balance. How large are the monthly payments?
8. Which of the following provides the greatest annual interest?
a. 10% compounded annually
b. 9.5% compounded monthly c. 9% compounded daily
9. If you place $50 in a savings account with an interest rate of 7% compounded weekly, what
will the investment be worth at the end of five years (round to nearest dollar)?
10. What is the annual compounded interest rate of an investment with a stated interest rate of
6% compounded quarterly for 7 years (round to the nearest .1%)?
11. If you put $600 in a savings account that yields an 8% rate of interest compounded weekly,
what will the investment be worth in 37 weeks (round to the nearest dollar)?
12. What is the value of $750 invested at 7.5% compounded quarterly for 4.5 years (round to
13. If you put $900 in a savings account that yields 10% compounded semi-annually, how
much money will you have in the account in three years (round to nearest dollar)?
14. Which o