in each of the cases shown in the following table to estimate, to the nearest year,

how long it would take an initial deposit, assuming no withdrawals,

a. To double.

b. To quadruple.

Case Interest rate

A 7%

B 40

C 20

D 10

P4–4

P4-4 Future values For each of the cases shown in the following table, calculate the

future value of the single cash flow deposited today that will be available at the end

of the deposit period if the interest is compounded annually at the rate specified over

the given period.

Case Single cash flow Interest rate Deposit period (years)

A $ 200 5% 20

B 4,500 8 7

C 10,000 9 10

D 25,000 10 12

E 37,000 11 5

F 40,000 12 9

P4–11 Present values For each of the cases shown in the following table, calculate the

present value of the cash flow, discounting at the rate given and assuming that the

cash flow is received at the end of the period noted.

Single cash End of

Case flow Discount rate period (years)

A $ 7,000 12% 4

B 28,000 8 20

C 10,000 14 12

D 150,000 11 6

E 45,000 20 8

P4–12 Present value concept

Answer each of the following questions.

a. What single investment made today, earning 12% annual interest, will be worth

$6,000 at the end of 6 years?

b. What is the present value of $6,000 to be received at the end of 6 years if the

discount rate is 12%?

c. What is the most you would pay today for a promise to repay you $6,000 at the

end of 6 years if your opportunity cost is 12%?

d. Compare, contrast, and discuss your findings in parts a through c.

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