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Chapter 3 The Time Value of Money
TRUE/FALSE
interest earned previously.
future value of a dollar.
rate of interest is greater than 2 percent.
for ten years is the same as $1,000 today.
that is an “ordinary annuity” and not an “annuity due.”
for ten years exceeds $1,000.
number of years increases.
number of years increases.
to 5 percent increases the present value of an annuity.
to bring together the present and the future.
present value of an ordinary annuity.
the future value of an annuity due.
by the frequency of compounding.
MULTIPLE CHOICE
1. increases with higher interest rates
2. decreases with higher interest rates
3. increases as the time period increases
4. decreases as the time period increases
a. 1 and 3
b. 1 and 4
c. 2 and 3
d. 2 and 4
a. rising annual payments
b. random payments
c. equal payments
d. unequal payments
1. increases as the interest rate increases
2. decreases as the interest rate increases
3. increases as the time period increases
4. decreases as the time period increases
a. 1 and 3
b. 1 and 4
c. 2 and 3
d. 2 and 4
a. expresses the present in the future
b. brings the future back to the present
c. is synonymous with compounding
d. depends on the rate of interest
1. larger the higher the rate of interest
2. smaller the higher the rate of interest
3. larger the greater the number of years
4. smaller the greater the number of years
a. 1 and 3
b. 1 and 4
c. 2 and 3
d. 2 and 4
7 percent?
a. $100 compounded for three years
b. the future value of a $100 annuity for three years
c. the present value of $100 after three years
d. the present value of a $100 annuity
1. larger the greater the rate of interest
2. smaller the greater the rate of interest
3. larger as the number of years increases
4. smaller as the number of years increases
a. 1 and 3
b. 1 and 4
c. 2 and 3
d. 2 and 4
8 percent?
a. $100 to be received after five years
b. the present value of an annuity of $100 for
five years
c. $100 received in the present
d. $100 received for two years
a. the present value of an annuity
b. the margin required on a stock purchase
c. the future value of $100 deposited in a bank
d. the present value of a lump sum
1. the annual growth rate in dividends
2. the amount in an IRA account after ten years
3. the tax owed on a capital gain
a. 1 and 2
b. 1 and 3
c. 2 and 3
d. only 2
1. the annuity is an ordinary annuity
2. the annuity is an annuity due
3. the payments are made at the beginning of the year
4. the payments are made at the end of the year
a. 1 and 3
b. 1 and 4
c. 2 and 3
d. 2 and 4
PROBLEMS
1. An investor expects the price of a stock to double after
eight years. What is the expected annual rate of growth?
2. If you open an IRA and invest $3,000 a year (at the end
of the year), how much will be in the account after
twenty-five years if the funds earn 5 percent annually? How
much would be in the account if payments were made at the
beginning of the year?
3. A state's lottery winner is promised $200,000 a year for
twenty years (starting at the end of the first year). How
much must the state invest now to guarantee the prize if
the state can earn annually 7 percent on its funds? How
much must the state invest if the annual payments are to be
made at the beginning of the year?
4. A homeowner has a ten-year home-improvement loan for
$36,875. What are the annual payments required by the loan
if the annual rate of interest is 4 percent?
5. You wish to have $100,000 after ten years for a major
purchase such as a boat. How much must you invest at the
end of each year if you earn 8 percent annually on your
funds?
6. Your uncle plans to leave you an inheritance of
$200,000. If his life expectancy is twenty years, what is
your inheritance currently worth if the anticipated return
on investments is 9 percent?
7. An investment offers $10,000 at the end of each year for
ten years. (a) If you can earn 5 percent annually, what is
this investment worth today? (b) If you do not spend the
annual payment but invest it at 5 percent, how much will
you have after the ten years have lapsed?
8. AIR National's capacity is 120 passengers per flight. It
currently carries 74 passengers per flight. Growth in
passengers is expected to be 6 percent annually. New plans
will have to be ordered when the company is carrying 90
percent of capacity. How long will it be before the firm
must order new planes?
9. A firm currently earns $1.00 per share. A financial
analyst believes that earnings will grow annually at the
rate of 10 percent for five years and then decline to 5
percent. What are the expected earnings after ten years?
10. Worker A annually invests $1,000 in an IRA for nine
years (ages 27 through 35) and never makes another
contribution. Worker B annually invests $1,000 in an IRA
for thirty years (ages 36 through 65). Which worker will
have more in his or her account when he or she retires if
they both earn 8 percent on their investments?
11. A piece of rental property will generate $10,000 a year
for five years, $12,000 for the next five years, and then
be sold at the end of the tenth year for $100,000. If you
can earn 10 percent on your funds, what is the maximum you
should pay for the property?
12. You are hurt in a car accident and your lawyer wins a
$100,000 settlement to be distributed as follows:
$20,000 immediate payment
$5,000 a year for ten years
$30,000 after ten years.
If the lawyer's fee is $10,000, what is the value of this
settlement if the interest rate is 6 percent?
13. Your brother, who is prone to bearing substantial risk,
suggests that you buy a security for $10,000 that promises
to pay you $100,000 at the end of 15 years. What is the
implied annual return or yield on this investment?
14. EEM, INC has a $1,000,000 debt outstanding that is due
after 15 years. The contract required that after five
years, the firm must set aside annually an amount so the
debt is retired in full at maturity. If EEM can earn 8
percent on invested funds, how much must the company set
aside each year?
15. A firm has a $1,000,000 debt (e.g., a bond)
outstanding that matures after 10 years. The sinking fund
requires the firm to set aside annually an amount so the
debt may be retired at maturity. If the firm can earn 10%
annually on these funds, how much must it invest annually
to meet the sinking fund?
16. A state lotto awarded a prize of $560,000 a year for
the next 20 years starting today. If the state sold
$21,900,000 in lotto tickets, what proportion of the sales
will the state distribute if it earns 8% annually on
invested funds?
17. You purchase a building for $10,000,000 and lease it
for $2,000,000 a year for four years (i.e., collect annual
rent payments). At the end of the four years, you plan to
sell the building. If you want to earn 10 percent on your
investment, how much must you receive from the sale?
SOLUTIONS TO PROBLEMS
