COMPREHENSIVE/SPREADSHEET
PROBLEM
2-41 Time value of money Answer the following questions:
a. Find the FV of $1,000 after 5 years earning a rate of 10 percent annually.
b. What would the investment’s FV be at rates of 0 percent, 5 percent, and 20 percent
after 0, 1, 2, 3, 4, and 5 years?
c. Find the PV of $1,000 due in 5 years if the discount rate is 10 percent.
d. What is the rate of return on a security that costs $1,000 and returns $2,000 after 5
years?
e. Suppose California’s population is 30 million people, and its population is
expected to grow by 2 percent annually. How long would it take for the popula-
tion to double?
f. Find the PV of an ordinary annuity that pays $1,000 each of the next 5 years if the
interest rate is 15 percent. What is the annuity’s FV?
g. How would the PV and FV of the above annuity change if it were an annuity due?
h. What would the FV and the PV be for $1,000 due in 5 years if the interest rate were
10 percent, semiannual compounding?
i. What would the annual payments be for an ordinary annuity for 10 years with a PV
of $1,000 if the interest rate were 8 percent? What would the payments be if this
were an annuity due?
j. Find the PV and the FV of an investment that pays 8 percent annually and makes
the following end-of-year payments:
k. Five banks offer nominal rates of 6 percent on deposits, but A pays interest annually,
B pays semiannually, C quarterly, D monthly, and E daily.
(1) What effective annual rate does each bank pay? If you deposited $5,000 in each
bank today, how much would you have at the end of 1 year? 2 years?
(2) If the banks were all insured by the government (the FDIC) and thus equally
risky, would they be equally able to attract funds? If not, and the TVM were the
only consideration, what nominal rate would cause all the banks to provide the
same effective annual rate as Bank A?
(3) Suppose you don’t have the $5,000 but need it at the end of 1 year. You plan to
make a series of deposits, annually for A, semiannually for B, quarterly for C,
monthly for D, and daily for E, with payments beginning today. How large must
the payments be to each bank?
(4) Even if the 5 banks provided the same effective annual rate, would a rational
investor be indifferent between the banks?
l. Suppose you borrowed $15,000. The loan’s annual interest rate is 8 percent, and it
requires 4 equal end-of-year payments. Set up an amortization schedule that shows
the annual payments, interest payments, principal repayments, and beginning and
ending loan balances.
10 2 3
$400$200$100