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5-2 Future value calculation Without referring to the preprogrammed function on your
financial calculator, use the basic formula for future value along with the given
interest rate, r, and the number of periods, n, to calculate the future value of $1 in
each of the cases shown in the following table.
Case Interest rate, r Number of periods, n
A 12% 2
B 6 3
C 9 2
D 3 4
P5–3 Future value You have $100 to invest. If you can earn 12% interest, about how
long does it take for your $100 investment to grow to $200? Suppose the interest
rate is just half that, at 6%. At half the interest rate, does it take twice as long to
double your money? Why or why not? How long does it take?
P5–13 Time value Jim Nance has been offered an investment that will pay him $500 three
years from today.
a. If his opportunity cost is 7% compounded annually, what value should he place
on this opportunity today?
b. What is the most he should pay to purchase this payment today?
c. If Jim can purchase this investment for less than the amount calculated in part a,
what does that imply about the rate of return that he will earn on the investment?
P5-20 Present value of an annuity Consider the following cases.
Case Amount of annuity Interest rate Period (years)
A $ 12,000 7% 3
B 55,000 12 15
C 700 20 9
D 140,000 5 7
E 22,500 10 5
a. Calculate the present value of the annuity assuming that it is
(1) An ordinary annuity.
(2) An annuity due.
b. Compare your findings in parts a(1) and a(2). All else being identical, which type
of annuity—ordinary or annuity due—is preferable? Explain why.
P5-30 Value of mixed streams Find the present value of the streams of cash flows shown
in the following table. Assume that the firm’s opportunity cost is 12%.
Year Cash flow Year Cash flow Year Cash flow
1 -$2,000 1 $10,000 1-5 $10,000/yr
2 3,000 2–5 5,000/yr 6–10 8,000/yr
3 4,000 6 7,000
P5–36 Changing compounding frequency Using annual, semiannual, and quarterly compounding
periods for each of the following, (1) calculate the future value if $5,000 is
deposited initially, and (2) determine the effective annual rate (EAR).
a. At 12% annual interest for 5 years.
b. At 16% annual interest for 6 years.
c. At 20% annual interest for 10 years.
P5–43 Creating a retirement fund To supplement your planned retirement in exactly
42 years, you estimate that you need to accumulate $220,000 by the end of 42 years
from today. You plan to make equal, annual, end-of-year deposits into an account
paying 8% annual interest.
a. How large must the annual deposits be to create the $220,000 fund by the end
of 42 years?
b. If you can afford to deposit only $600 per year into the account, how much will
you have accumulated by the end of the forty-second year?
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