# Time Value of Money – More Practice Problems – Answers

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```					Time Value of Money – More Practice Problems                             ANSWERS
Finance 350
1.   If you borrow \$200 today @ 10%, how much must you pay back after 1 year? 2
years? 3 years?
A: These are future value questions:
i) \$220.00       ii) \$242.00             iii) \$266.20

2.   In one year we need \$220. How much must we invest today at 10%?
A: PV = \$200

3.   In three years we need \$266.20. How much must we invest today at 10%?
A: PV = \$200

4.   I want to trek in the Chilean Andes in 4 years. If I estimate that the
trip will cost me \$5,000 and the interest rate will be 8% over the period,
how much must I invest today?
A: PV = \$3,675.15

5.   I would also like to take a jaunt in Nepal in 2 years. Estimated costs are
\$3,000, and the interest rate I can earn on my investment today is still
8%. How much must I invest today?
A: PV = \$2,572.02

6.   Suppose that one year from now you finally decide to join me in my
travels. How much must you invest at the end of year 1, for both trips to
Chile and Nepal?
A: i) PV1 = \$3,969.16                    ii) PV1 = \$2,777.77

7.   If we expect interest rates to change over the next four years (r1=8%,
r2=10%, r3=r4= 12%), how much do we need to invest today to travel to
Chile and Nepal?
A: i) PVChile = 5000/[ (1.12)2(1.10)(1.08)] = \$3,355.19
ii) PVNepal = 3000/[ (1.10)(1.08)] = \$2,525.25

8.   From #5, if I have \$2,155 to invest today, what interest rate must I earn
on my investment to attain the \$3,000 required for the trip?
A: Use formula for r given in class: r = 17.99%

9.   \$100 per year for 3 years, r= 10%. What is the future value?
A: FV(annuity) = FVA = 100 * FVIFA(10%, 3 yrs) = \$331.00

10. \$100 per year for 3 years, r=10%. What is the present value?
A: PV(annuity) = PVA = 100 * PVIFA(10%, 3 yrs) = \$248.69

11. \$100 per year forever. r=10%. What is the present value?
A: PV(perpetuity) = C/r = 100/.10 = \$1,000

12. Suppose you hit the lottery and decide to endow a faculty position at the
UW Business School. Salaries are currently \$100,000 per year. If the
interest rate is 10%, how much must you donate today? Suppose salaries are
expected to grow 4% a year; now how much must you donate?
A: PV(perpetuity w/ growth) = C/(r-g) = 100,000/(.10-.04) = \$1,666,667
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Time Value of Money – More Practice Problems                           ANSWERS
Finance 350
13. \$10,000 five-year Certificate of Deposit, r=8%, interest compounded
quarterly. What is the effective annual rate? Future value?
A: i) EAR = (1+(.08/4))4–1 = 0.08243 or 8.243%
ii) FV = 10,000[1+(.08/4)]4*5 = \$14,859.47

14. \$10,000 five-year Certificate of Deposit, r=8%, interest compounded
continuously. What is the effective annual rate? Future value?
A: i) EAR = e.08–1 = .0833 or 8.33%
ii) FV = 10,000[1+.0833]5 = \$14,918.25

15. Consider two cash flows, both with present values of \$1,000 when r=10%.
Cash flow 1 is comprised of \$162.74 per year for 10 years. Cash flow 2 is
comprised of \$263.80 per year for 5 years. What happens if the interest
rates fall to 8%?
A: i) PVA = \$162.74* PVIFA(8%, 10 yrs) = \$1,092.00
ii) PVA = \$263.80* PVIFA(8%, 5 yrs) = \$1,053.28
Both annuities’ PVs increase. Notice the longer annuity enjoys a greater
% increase in value. This fact will be further developed in the Bonds
topic (Topic 4).

16. What happens to cash flow 2 if r increases to 12%?
A: PVA = \$263.80* PVIFA(12%, 5 yrs) = \$950.94

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