You need $28,974 at the end of 10 years, and your only investment outlet is an 8 percent
long-term certificate of deposit (compounded annually). With the certificate of deposit, you
make an initial investment at the beginning of the first year.
Difference between old and new payments
P.V. of difference Appendix D
You are chairperson of the investment fund for the Eastern Football League. You are asked
to set up a fund of semiannual payments to be compounded semiannually to
Les Moore retired as president of Goodman Snack Foods Company but is currently on a
consulting contract for $35,000 per year for the next 10 years.
If Mr. Moores opportunity cost (potential return) is 10 percent, what is the present
value of his co
Jack Hammer invests in a stock that will pay dividends of $2.00 at the end of the first year;
$2.20 at the end of the second year; and $2.40 at the end of the third year. Also, he believes
that at the end of the third year he will be able to sell the
Linda (from problem 44) is now 18 years old (five years have passed), and she wants to get
married instead of going to school. Your parents have accumulated the necessary funds for
Instead of her schooling,
Polly Graham will receive $12,000 a year for the next 15 years as a result of her patent.
If a 9 percent rate is applied, should she be willing to sell out her future rights now
PVA = A PVIFA (9%, 20 periods)
Bridget Jones has a contract in which she will receive the following payments for the next
five years: $1,000, $2,000, $3,000, $4,000, and $5,000. She will then receive an annuity
of $8,500 a year from the end of the 6th through the end of the 15th ye
Your uncle offers you a choice of $30,000 in 50 years or $95 today. If money is discounted
at 12 percent, which should you choose?
PV = FV PVIF (12%, 50 periods)
PV = $30,000 .003 = $90
Choose $95 today.
Your aunt offe
You wish to retire after 18 years, at which time you want to have accumulated enough
money to receive an annuity of $14,000 a year for 20 years of retirement. During the period
before retirement you can earn 11 percent annually, while after retirement
How much would you have to invest today to receive:
$15,000 in 8 years at 10 percent?
$20,000 in 12 years at 13 percent?
$6,000 each year for 10 years at 9 percent?
$50,000 each year for 50 years at 7 percent?
Appendix B (a a
Morgan Jennings, a geography professor, invests $50,000 in a parcel of land that is
expected to increase in value by 12 percent per year for the next five years. He will take the
proceeds and provide himself with a 10-year annuity. Assuming a 12 perce
CP 9-1. (Continued)
+ .70 $3,000,000 = $2,100,000
Total value of Offer I
Present value of deferred annuity
Present value of $3 million bonus
PV of vacation = $12,435
Remaining funds for graduate school
Funds available 3 years later for graduate school:
Number of years of graduate education
with i = 10%, n = 4 for 3.170 the answer i
Dr. I. N. Stein has just invested $6,250 for his son (age one). The money will be used for
his sons education 17 years from now. He calculates that he will need $50,000 for his sons
education by the time the boy goes to school. What rate of return wil
CP 9-1. (Continued)
Total value of Offer II
Future value of an annuity due (Appendix C)
8 years semiannually
n = 16 + 1 = 17
i = 10%/2 = 5%
FVIFA = 25
b. First determine how much the old payments are equal to after
4 periods at 4%. Appendix C.
Then determine how much this value will grow to after 16
periods at 5%. Appendix A.
Subtract this value from $100,000 to determine how much you
On January 1, 2002, Mike Irwin, Jr., bought 100 shares of stock at $14 per share. On
December 31, 2008, he sold the stock for $21 per share. What is his annual rate of return?
Interpolate to find the exact answer.
Select $24,000 to be received in eight years.
Revised answers based on 12%.
(first alternative) Present value of $10,000 received today: $10,000
(second alternative) Present value of annuity of $2,000 for 8 years:
If you borrow $15,618 and are required to pay back the loan in seven equal annual
installments of $3,000, what is the interest rate associated with the loan?
Interest rate = 8 percent
Cal Lury owes $10,000 now. A lender
Ester Seals has just given an insurance company $41,625. In return, she will receive an
annuity of $5,000 for 15 years. At what rate of return must the insurance company invest
this $41,625 to make the annual payments? Interpolate.
You invest $3,000 a year for three years at 12 percent.
What is the value of your investment after one year? Multiply $3,000 1.12.
What is the value of your investment after two years? Multiply your answer to part a
Adjust the annual formula for a future value of a single amount at 12 percent for
10 years to a semiannual compounding formula. What are the interest factors
(FVIF) before and after? Why are they different?
The more frequent compounding under the sem