Chapter 5 Time Value of Money 155
GROWTH RATES Shalit Corporation’s 2008 sales were $12 million. Its 2003 sales were
$6 million.
a. At what rate have sales been growing?
b. Suppose someone made this statement: “Sales doubled in 5 years. This represents a
growth of 100% in 5 years; so dividing 100% by 5, we find the growth rate to be 20%
per year.” Is that statement correct?
EFFECTIVE RATE OF INTEREST Find the interest rates earned on each of the following:
a. You borrow $700 and promise to pay back $749 at the end of 1 year.
b. You lend $700 and the borrower promises to pay you $749 at the end of 1 year.
c. You borrow $85,000 and promise to pay back $201,229 at the end of 10 years.
d. You borrow $9,000 and promise to make payments of $2,684.80 at the end of each year
for 5 years.
TIME FOR A LUMP SUM TO DOUBLE How long will it take $200 to double if it earns the
following rates? Compounding occurs once a year.
a. 7%
b. 10%
c. 18%
d. 100%
FUTURE VALUE OF AN ANNUITY Find the future values of these ordinary annuities.
Compounding occurs once a year.
a. $400 per year for 10 years at 10%
b. $200 per year for 5 years at 5%
c. $400 per year for 5 years at 0%
d. Rework Parts a, b, and c assuming they are annuities due.
PRESENT VALUE OF AN ANNUITY Find the present values of these ordinary annuities.
Discounting occurs once a year.
a. $400 per year for 10 years at 10%
b. $200 per year for 5 years at 5%
c. $400 per year for 5 years at 0%
d. Rework Parts a, b, and c assuming they are annuities due.
PRESENT VALUE OF A PERPETUITY What is the present value of a $100 perpetuity
if the interest rate is 7%? If interest rates doubled to 14%, what would its present
value be?
EFFECTIVE INTEREST RATE You borrow $85,000; the annual loan payments are $8,273.59
for 30 years. What interest rate are you being charged?
UNEVEN CASH FLOW STREAM
a. Find the present values of the following cash flow streams at 8% compounded
annually.
0 2 3
$300
$100
$400
$400
$400
$400
$400
$400
$100
$300
$0
$0
Stream A
Stream B
1 4 5
b. What are the PVs of the streams at 0% compounded annually?
FUTURE VALUE OF AN ANNUITY Your client is 40 years old; and she wants to begin sav-
ing for retirement, with the first payment to come one year from now. She can save $5,000
per year; and you advise her to invest it in the stock market, which you expect to provide
an average return of 9% in the future.
a. If she follows your advice, how much money will she have at 65?
b. How much will she have at 70?
c. She expects to live for 20 years if she retires at 65 and for 15 years if she retires at 70. If
her investments continue to earn the same rate, how much will she be able to with-
draw at the end of each year after retirement at each retirement age?
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