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9-30. Solution:
.a
10
1
(1 )
1
$28,974 (1.08)
$13, 420.57
n
PV FV
i
PV
PV
= ´ +
= ´
=
.b
10
(1 ) 1
$28,974
(1.08) 1
.08
$2,000.06
A
n
FV
A
i
i
A
A
=+ -
=-
=
Calculator Solution:
(a)
N I/Y PV PMT FV
Answer: $13,420.57
(b)
Answer: $2,000.06
a. Appendix B
b. Appendix C
31. Quarterly compounding (LO9-5) Beverly Hills started a paper route on January 1. Every
three months, she deposits $550 in her bank account, which earns 8 percent annually but is
compounded quarterly Four years later, she used the entire balance in her bank account to
invest in an investment at 7 percent annually. How much will she have after three more
years?
9-31. Solution:
Quarterly deposits for four years
4
16
1 1
4
(1.02) 1
$550 .02
$10, 251.61
n
i
FV A
i
FV
FV
æ ö
+ -
ç ÷
è ø
= ´
-
= ´
=
Investment growth over three years
3
(1 )
$10, 251.61 (1.07)
$12,558.66
n
FV PV i
FV
FV
= ´ +
= ´
=
Step one:
N I/Y PV PMT FV
Answer: $10,251.61
Step two:
N I/Y PV PMT FV
Answer: $12,558.66
Appendix C
Appendix A
32. Yield (LO9-4) Franklin Templeton has just invested $9,260 for his son (age one). This
money will be used for his son’s education 18 years from now. He calculates that he will
need $71,231 by the time the boy goes to school. What rate of return will Mr. Templeton
need in order to achieve this goal?
9-32. Solution:
[ ]
18
18
11
18 18 18
1
(1 )
1 $9,260
(1 ) $71,231
(1 ) 7.692
(1 ) 7.692
1 1.12
.12
n
PV
i FV
i
i
i
i
i
=
+
=
+
+ =
é ù
+ =
ë û
+ =
=
Franklin Templeton needs a 12 percent rate to achieve his goal of $71,231.
Calculator Solution:
N I/Y PV PMT FV
Answer: 12.00
Appendix B
IF
IF
PV
PV = (18 periods)
FV
$9, 260
PV = .130 Rate of return 12%
$71, 231 = =
IF
IF
FV
FV (18 periods)
PV
$71, 231
FV 7.69 Rate of return 12%
$9, 260
=
= = =
33. Yield with interpolation (LO9-4) Mr. Dow bought 100 shares of stock at $14 per share.
Three years later, he sold the stock for $20 per share. What is his annual rate of return?
9-33. Solution:
3
3
1
13
33
$14 100
$1, 400
$20 100
$2,000
(1 )
(1 )
$2,000
(1 ) $1, 400
10
(1 ) 7
10
((1 ) ) 7
1 1.1262
12.62%
n
n
PV
PV
FV
FV
FV PV i
FV
i
PV
i
i
i
i
i
= ´
=
= ´
=
= ´ +
+ =
+ =
+ =
é ù
+ =ê ú
ë û
+ =
=
IF
PV
PV FV
=
IF
$14
PV .700
$20
= =
Return is between 12–13 percent for three
years.
IF
IF
PV at 12% .712
PV at 13% .693
.019
-
IF
IF
PF at 12% .712
PV computed .700
.012
-
34. Yield with interpolation (LO9-4) C. D. Rom has just given an insurance company
$35,000. In return, he will receive an annuity of $3,700 for 20 years.
At what rate of return must the insurance company invest this $35,000 in order to make
the annual payments? Interpolate.
9-34. Solution:
Calculator Solution:
N I/Y PV PMT FV
Answer: 8.51%
Appendix D
IFA A
PV PV / A (20 periods)
$35,000 / $3,700
9.459 is between 8% and 9% for 20 periods
=
=
=
IFA
IFA
PV at 8% 9.818
PV at 9% 9.129
.689
-
IFA
IFA
PV at 8% 9.818
PV computed 9.459
.359
-
35. Betty Bronson has just retired after 25 years with the electric company. Her total pension
funds have an accumulated value of $180,000, and her life expectancy is 15 more years.
Her pension fund manager assumes he can earn a 9 percent return on her assets. What will
be her yearly annuity for the next 15 years?
9-35. Solution:
15
1
1(1 )
1
1(1 )
$180,000
1
1(1.09)
.09
$22,330.60
n
A
A
n
i
PV A
i
PV
A
i
i
A
A
æ ö
-
ç ÷
+
= ´ ç ÷
ç ÷
ç ÷
è ø
=æ ö
-
ç ÷
+
ç ÷
ç ÷
ç ÷
è ø
=æ ö
-
ç ÷
ç ÷
ç ÷
ç ÷
è ø
=
Calculator Solution:
N I/Y PV PMT FV
Answer: $22,330.60
Appendix D
A PV / PV (9%, 15periods)
=
9-36. Solution:
Part 1
5
(1 )
$50,000 (1.12)
$88,117.08
n
FV PV i
FV
FV
= ´ +
= ´
=
Part 2
10
1
1(1 )
1
1(1 )
$88,117.08
1
1(1.12)
.12
$15,595.33
n
A
A
n
i
PV A
i
PV
A
i
i
A
A
æ ö
-
ç ÷
+
= ´ ç ÷
ç ÷
ç ÷
è ø
=æ ö
-
ç ÷
+
ç ÷
ç ÷
ç ÷
è ø
=æ ö
-
ç ÷
ç ÷
ç ÷
ç ÷
è ø
=
Calculator Solution:
Step one:
N I/Y PV PMT FV
Step two:
N I/Y PV PMT FV
Answer: $15,595.33
Appendix A
Appendix D
37. Solving for an annuity (LO9-4) You wish to retire in 14 years, at which time you want to
have accumulated enough money to receive an annual annuity of $17,000 for 19 years after
retirement. During the period before retirement you can earn 8 percent annually, while after
retirement you can earn 10 percent on your money.
What annual contributions to the retirement fund will allow you to receive the $17,000
annuity?
9-37. Solution:
Part 1
19
1
1(1 )
1
1(1.10)
$17,000 .10
$142,203.64
n
A
A
A
i
PV A
i
PV
PV
æ ö
-
ç ÷
+
= ´ ç ÷
ç ÷
ç ÷
è ø
æ ö
-
ç ÷
= ´ ç ÷
ç ÷
ç ÷
è ø
=
Part 2
14
(1 ) 1
(1 ) 1
$142,203.64
(1.08) 1
.08
$5,872.56
n
A
A
n
i
FV A
i
FV
A
i
i
A
A
æ ö
+ -
= ´ ç ÷
è ø
=æ ö
+ -
ç ÷
è ø
=æ ö
-
ç ÷
è ø
=
Calculator Solution:
Determine the present value of a 14-year annuity during retirement:
To determine the annual deposit into an account earning 8% that is necessary to accumulate
$142,203.64 after 14 years, solve for the annuity:
N I/Y PV PMT FV
Determine the present value of an annuity during retirement:
Appendix D
A IFA
PV A PV (10%, 19 years)
$17,000 8.365 $142,205
= ´
= ´ =
To determine the annual deposit into an account earning 8 percent
that is necessary to accumulate $142,205 after 14 years, use the
future value of an annuity table. See Appendix C.
A IFA
A FV / FV (8%, 14 years)
$142,205 = $5,872.60 annual contribution
24.215
=
=
38. Del Monty will receive the following payments at the end of the next three years: $2,000,
$3,500, and $4,500. Then, from the end of the 4th through the end of the 10th year, he will
receive an annuity of $5,000 per year. At a discount rate of 9 percent, what is the present
value of all three future benefits?
