Select $2,200 received for nine years.
(first alternative) Present value of $7,500 received now:
$7,500
(second alternative) Present value of annuity of $2,200 for nine
years: Appendix D
A IFA
IFA
PV A×PV
$2, 200 PV (10%, 9 years)
$2, 200 5.759
$12,670
=
= ´
= ´
=
(third alternative) Present value of $31,000 received in nine
years: Appendix B
IF
IF
PV FV×PV
$31,000×PV (10%, 9 years)
$31,000×.424
$13,144
=
=
=
=
Select $31,000 to be received in nine years.
9-29. (Continued)
Revised answers based on 11 percent.
(second alternative) Present value of annuity of $2,200 at 11
percent for nine years: Appendix D
A IFA
IFA
PV A PV
$2, 200 PV (11%, 9 years)
$2, 200 5.537
$12,181
= ´
= ´
= ´
=
(third alternative) Present value of $31,000 received in nine years
at 11 percent: Appendix B
IF
IF
PV = FV×PV
= $31,000×PV (11%, 9 years)
= $31,000×.391
= $12,121
Select $2,200 a year for nine years. As the interest rate (discount
rate) increases, the present value declines.
30. 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.
a. What single payment could be made at the beginning of the first year to achieve this
objective?
b. What amount could you pay at the end of each year annually for 10 years to achieve
this same objective?
9-30. Solution:
.a
10
1
(1 )
1
$28,974 (1.08)
$13, 420.57
n
PV FV
i
PV
PV
= ´ +
= ´
=
.b
Calculator Solution:
(a)
N I/Y PV PMT FV
(b)
N I/Y PV PMT FV
a. Appendix B
PV = FV × PVIF (8%, 10 periods)
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
= ´ +
= ´
=
Calculator Solution:
Step one:
N I/Y PV PMT FV
Answer: $10,251.61
Step two:
N I/Y PV PMT FV
Appendix C
FVA = A × FVIFA (2%, 16 periods)
Appendix A
FV = PV × FVIF (7%, 3 periods)
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.
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 = =
Or
Alternative solution
Appendix A
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
+ =
=
Calculator Solution:
N I/Y PV PMT 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
–
12% + (.012/.019) (1%)
12% + .632 (1%)
12.63%
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
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
–
8% + (.359/.689) (1%)
8% + .521 (1%) = 8.52%
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?