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9-16. Solution:
20
1
1(1 )
1
1(1.10)
$19,500 .10
$166,014.49
n
A
A
A
i
PV A
i
PV
PV
-+
= ´
-
= ´
=
Carrie Tune should not accept $160,000 for the
future rights because they are worth more than that.
Calculator Solution:
N I/Y PV PMT FV
Answer: $166,014.49
Appendix D
17. The Clearinghouse Sweepstakes has just informed you that you have won $1 million. The
amount is to be paid out at the rate of $20,000 a year for the next 50 years. With a discount
rate of 10 percent, what is the present value of your winnings?
9-17. Solution:
50
1
1(1 )
1
1(1.10)
$20,000 .10
$198, 296.29
n
A
A
A
i
PV A
i
PV
PV
-+
= ´
-
= ´
=
Calculator Solution:
N I/Y PV PMT FV
Answer: $198,296.29
Appendix D
$1.5 million a year for the next 19 years plus an additional lump sum payment of $12.5
million after 19 years. The discount rate is 14 percent. What is the current value of her
winnings?
9-18. Solution:
Annuity Part
19
1
1(1 )
1
1(1.14)
$1,500,000 .14
$9,825,553.24
n
A
A
A
i
PV A
i
PV
PV
-+
= ´
-
= ´
=
Lump Sum Part
19
1
(1 )
1
$12,500,000 (1.14)
$1,036,854.55
n
PV FV
i
PV
PV
= ´ +
= ´
=
Total Value
Calculator Solution:
First part:
N I/Y PV PMT FV
Answer: $9,825,553.24
Second part:
N I/Y PV PMT FV
Answer: $1,036,854.55
Appendix D
Appendix B
19. Al Rosen invests $25,000 in a mint condition 1952 Mickey Mantle Topps baseball card. He
expects the card to increase in value 12 percent per year for the next 10 years. How much
will his card be worth after 10 years?
9-19. Solution:
10
(1 )
$25, 000 (1.12)
$77,646.21
n
FV PV i
FV
FV
= ´ +
= ´
=
Calculator Solution:
Part one:
N I/Y PV PMT FV
Answer: $77,646.21
Appendix A
20. Future value (LO9-2) Christy Reed made a $2,000 deposit in her savings account on her
21st birthday, and she has made another $2,000 deposit on every birthday since then. Her
account earns 7 percent compounded annually. How much will she have in her account
after she makes the deposit on her 32nd birthday?
9-20. Solution:
12
(1 ) 1
(1.07) 1
$2,000 .07
$35, 776.90
n
A
A
A
i
FV A
i
FV
FV
+ -
= ´
-
= ´
=
Calculator Solution:
N I/Y PV PMT FV
Answer: $35,776.90
Appendix C
21. Future value (LO9-2) At a growth (interest) rate of 10 percent annually, how long will it
take for a sum to double? To triple? Select the year that is closest to the correct answer.
9-21. Solution:
Tip To solving this problem
(1 )
2 1 (1.10)
2 (1.10)
ln(2) ln(1.1)
ln(2)
ln(1.1)
7.27 years
n
n
n
FV PV i
n
n
n
= ´ +
= ´
=
= ´
=
=
To Triple
(1 )
3 1 (1.10)
3 (1.10)
ln(3) ln(1.1)
ln(3)
ln(1.1)
11.53 years
n
n
n
FV PV i
n
n
n
= ´ +
= ´
=
= ´
=
=
Calculator Solution:
To double:
N I/Y PV PMT FV
N I/Y PV PMT FV
Answer: 11.53 years
Appendix A
22. Present value (LO9-3) If you owe $35,000 payable at the end of eight years, what amount
should your creditor accept in payment immediately if she could earn 13 percent on her
money?
9-22. Solution:
8
1
(1 )
1
$35,000 (1.13)
$13,165.60
n
PV FV
i
PV
PV
= ´ +
= ´
=
Calculator Solution:
N I/Y PV PMT FV
Answer: $13,165.60
Appendix B
PV = FV × PVIF (13%, 8 periods)
PV = $35,000 × .376 = $13,160
23. 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 stock for $33. What is the present
value of all future benefits if a discount rate of 11 percent is applied? (Round all values to
two places to the right of the decimal point.)
9-23. Solution:
First Dividend
1
1
(1 )
1
$2 (1.11)
$1.80
n
PV FV
i
PV
PV
= ´ +
= ´
=
Second Dividend
2
1
(1 )
1
$2.20 (1.11)
$1.79
n
PV FV
i
PV
PV
= ´ +
= ´
=
Third Dividend
3
1
(1 )
1
$2.40 (1.11)
n
PV FV
i
PV
= ´ +
= ´
Selling Price
3
1
(1 )
1
$33 (1.11)
$24.13
n
PV FV
i
PV
PV
= ´ +
= ´
=
Present Value Total
$24.13 Selling price
+ 1.80 First dividend
+ 1.79 Second dividend
+ 1.75 Third dividend
$29.47 Present total value
First dividend:
N I/Y PV PMT FV
Answer: $1.80
Second dividend:
N I/Y PV PMT FV
Answer: $1.79
Third dividend:
N I/Y PV PMT FV
Answer: $1.75
Selling price:
N I/Y PV PMT FV
Answer: $39.15
Appendix B
PV = FVIF
24. 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.
a. If Mr. Moore’s opportunity cost (potential return) is 10 percent, what is the present
value of his consulting contract?
b. Assuming Mr. Moore will not retire for two more years and will not start to receive
his 10 payments until the end of the third year, what would be the value of his
deferred annuity?
