Principles of Managerial Finance

CHAPTER 4 Time Value of Money 209

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4–57 Time to accumulate a given sum Manuel Rios wishes to determine how long it

will take an initial deposit of $10,000 to double.

a. If Manuel earns 10% annual interest on the deposit, how long will it take for

him to double his money?

b. How long will it take if he earns only 7% annual interest?

c. How long will it take if he can earn 12% annual interest?

d. Reviewing your findings in parts a, b,and c,indicate what relationship exists

between the interest rate and the amount of time it will take Manuel to dou-

ble his money?

4–58 Number of years—Annuities In each of the following cases, determine the

number of years that the given annual end-of-yearcash flow must continue in

order to provide the given rate of return on the given initial amount.

4–59 Time to repay installment loan Mia Salto wishes to determine how long it will

take to repay a loan with initial proceeds of $14,000 where annual end-of-year

installment payments of $2,450 are required.

a. If Mia can borrow at a 12% annual rate of interest, how long will it take for

her to repay the loan fully?

b. How long will it take if she can borrow at a 9% annual rate?

c. How long will it take if she has to pay 15% annual interest?

d. Reviewing your answers in parts a, b,and c,describe the general relationship

between the interest rate and the amount of time it will take Mia to repay the

loan fully.

CHAPTER 4 CASE Finding Jill Moran’s Retirement Annuity

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unrise Industries wishes to accumulate funds to provide a retirement annuity

for its vice president of research, Jill Moran. Ms. Moran by contract will

retire at the end of exactly 12 years. Upon retirement, she is entitled to receive an

annual end-of-year payment of $42,000 for exactly 20 years. If she dies prior to

the end of the 20-year period, the annual payments will pass to her heirs. During

the 12-year “accumulation period” Sunrise wishes to fund the annuity by mak-

ing equal annual end-of-year deposits into an account earning 9% interest. Once

the 20-year “distribution period” begins, Sunrise plans to move the accumulated

monies into an account earning a guaranteed 12% per year. At the end of the

distribution period, the account balance will equal zero. Note that the first

Case Initial amount Annual cash flow Rate of return

A $ 1,000 $ 250 11%

B 150,000 30,000 15

C 80,000 10,000 10

D 600 275 9

E 17,000 3,500 6