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9-8. Solution:
a.
12
1
(1 )
1
$105,000 (1.08)
$41,696.94
n
PV FV
i
PV
PV
= ´ +
= ´
=
b.
9
1
(1 )
1
$105,000 (1.08)
$52,526.14
n
PV FV
i
PV
PV
= ´ +
= ´
=
Calculator Solution:
(a) & (b)
N I/Y PV PMT FV
Answer: $41,696.94
(c) & (d)
N I/Y PV PMT FV
Answer: $52,526.14
a. Appendix B
b. Appendix B
9. Present Value (LO9-3) You are going to receive $205,000 in 18 years. What is the
difference in present value between using a discount rate of 12 percent versus 9 percent?
9-9. Solution:
9% Rate
18
1
(1 )
1
$205,000 (1.09)
$43,458.72
n
PV FV
i
PV
PV
= ´ +
= ´
=
12% Rate
18
1
(1 )
1
$205,000 (1.12)
$26,658.12
n
PV FV
i
PV
PV
= ´ +
= ´
=
The Difference
Calculator Solution:
At 12%
N I/Y PV PMT FV
Answer: $26,658.12
At 9%
N I/Y PV PMT FV
Answer: $43,458.72
Appendix B
$205,000 $205,000
.130 (12%,18) .212 (9%,18)
$26, 650 $43, 460
The difference is $16,810
$43, 460
26,650
$16,810
-
10. How much would you have to invest today to receive
a. $15,000 in 8 years at 10 percent?
b. $20,000 in 12 years at 13 percent?
c. $6,000 each year for 10 years at 9 percent?
d. $50,000 each year for 50 years at 7 percent?
9-10. Solution:
a.
8
1
(1 )
1
$15,000 (1.10)
$6,997.61
n
PV FV
i
PV
PV
= ´ +
= ´
=
b.
12
1
(1 )
1
$20,000 (1.13)
$4,614.12
n
PV FV
i
PV
PV
= ´ +
= ´
=
c.
10
1
1(1 )
1
1(1.09)
$6,000 .09
$38,505.95
n
A
A
A
i
PV A
i
PV
PV
-+
= ´
-
= ´
=
d.
50
1
1(1 )
1
1(1.07)
$50,000 .07
$690,037.31
n
A
A
A
i
PV A
i
PV
PV
-+
= ´
-
= ´
=
Calculator Solution:
(a)
N I/Y PV PMT FV
Answer: $6,997.61
(b)
N I/Y PV PMT FV
Answer: $4,614.12
(c)
N I/Y PV PMT FV
Answer: $38,505.95
(d)
N I/Y PV PMT FV
Answer: $690,037.31
Appendix B (a and b)
PV = FV × PVIF
Appendix D (c and d)
11. Future value (LO9-2) If you invest $8,500 per period for the following number of periods,
how much would you have?
9-11. Solution:
a.
12
(1 ) 1
(1.10) 1
$8,500 .10
$181,766.41
n
A
A
A
i
FV A
i
FV
FV
+ -
= ´
-
= ´
=
b.
50
(1 ) 1
(1.09) 1
$8,500 .09
$6,928,210.23
n
A
A
A
i
FV A
i
FV
FV
+ -
= ´
-
= ´
=
Calculator Solution:
(a)
N I/Y PV PMT FV
Answer: $181,766.41
(b)
N I/Y PV PMT FV
Answer: $6,928,210.23
Appendix C
FVA = A × FV IFA
12. You invest a single amount of $10,000 for 5 years at 10 percent. At the end of 5 years you
take the proceeds and invest them for 12 years at 15 percent. How much will you have
after 17 years?
9-12. Solution:
After 5 Years
5
(1 )
$10,000 (1.10)
$16,105.10
n
FV PV i
FV
FV
= ´ +
= ´
=
After 17 Years
12
(1 )
$16,10.10 (1.15)
$86,166.31
n
FV PV i
FV
FV
= ´ +
= ´
=
Calculator Solution:
First step:
N I/Y PV PMT FV
Answer: $16,105.10
Second step:
N I/Y PV PMT FV
Answer: $86,166.31
Appendix A
Appendix A
13. Present value (LO9-3) Mrs. Crawford will receive $7,600 a year for the next 19 years
from her trust. If a 14 percent interest rate is applied, what is the current value of the future
payments?
9-13. Solution:
19
1
1(1 )
1
1(1.14)
$7,600 .14
$49, 782.80
n
A
A
A
i
PV A
i
PV
PV
-+
= ´
-
= ´
=
Calculator Solution:
N I/Y PV PMT FV
Answer: $49,782.80
Appendix D
14. Phil Goode will receive $175,000 in 50 years. His friends are very jealous of him. If the
funds are discounted back at a rate of 14 percent, what is the present value of his future
“pot of gold”?
9-14. Solution:
50
1
(1 )
1
$249.92
n
PV FV
i
PV
= ´ +
=
Answer: $249.92
Appendix B
15. Present value (LO9-3) Sherwin Williams will receive $18,500 a year for the next 25 years
as a result of a picture he has painted. If a discount rate of 12 percent is applied, should he
be willing to sell out his future rights now for $165,000?
9-15. Solution:
25
1
1(1 )
1
1(1.12)
$18,500 .12
$145,098.07
n
A
A
A
i
PV A
i
PV
PV
-+
= ´
-
= ´
=
Calculator Solution:
N I/Y PV PMT FV
Answer: $145,098.07
Appendix D
16. Carrie Tune will receive $19,500 for the next 20 years as a payment for a new song she has
written. If a 10 percent rate is applied, should she be willing to sell out her future rights
now for $160,000?
