APPENDIX A
Time Value of Money
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE A-1
(a) Interest = p X i X n
BRIEF EXERCISE A-2
(1) Case A 5% 3 periods (2) Case A 3% 8 periods
BRIEF EXERCISE A-3
FV = p X FV of 1 factor
BRIEF EXERCISE A-4
= $78,000 X 16.86994
BRIEF EXERCISE A-5
= ($5,000 X 2.40662) + ($1,000 X 28.13238)
BRIEF EXERCISE A-6
FV = p X FV of 1 factor
BRIEF EXERCISE A-7
(a) (b)
(1) 12% 7 periods
(2) 10% 20 periods
BRIEF EXERCISE A-8
(a) i = 10%
?
$25,000
0 1 2 3 4 5 6 7 8 9
$10,602.50 ($25,000 X .42410).
BRIEF EXERCISE A-8 (Continued)
(b) i = 9%
? $25,000 $25,000 $25,000 $25,000 $25,000 $25,000
0 1 2 3 4 5 6
($25,000 X 4.48592).
BRIEF EXERCISE A-9
i = 8%
? $750,000
0 1 2 3 4 5 6
($750,000 X .63017). Chaffee Company should therefore invest $472,627.50
to have $750,000 in six years.
BRIEF EXERCISE A–10
i = 6%
?
$450,000
0 1 2 3 4 5 6 7 8
$450,000 in eight years.
BRIEF EXERCISE A–11
i = 8%
? $46,000 $46,000 $46,000 $46,000 $46,000 $46,000
0 1 2 3 4 14 15
BRIEF EXERCISE A–12
i = 5%
? $80,000 $80,000 $80,000 $80,000 $80,000 $80,000
0 1 2 3 4 5 6
BRIEF EXERCISE A–13
i = 5%
? $300,000
Diagram
for
Principal
0 1 2 3 4 19 20
i = 5%
Diagram
for
Interest
0 1 2 3 4 19 20
$300,000 X 0.37689 (PV of $1 due in 20 periods
at 5% from Table 3) …………………………………………………….. $113,067*
Present value of interest to be received periodically
BRIEF EXERCISE A–14
as follows:
Present value of principal to be received at maturity:
$300,000 X .31180 (PV of $1 due in 20 periods
at 6% from Table 3) …………………………………………………….. $ 93,540*
BRIEF EXERCISE A–15
i = 6%
Diagram
for
Principal
i = 6%
Diagram
for
Interest
$65,000 X .70496 (PV of $1 due in 6 periods
at 6% from Table 3) ……………………………………………………. $45,822.40
Present value of interest to be received annually
*$65,000 X .04
BRIEF EXERCISE A–16
i = 4%
? $2,500,000
Diagram
for
Principal
0 1 2 3 4 14 15 16
i = 4%
? $75,000 $75,000 $75,000 $75,000 $75,000 $75,000 $75,000
Diagram
for
Interest
0 1 2 3 4 14 15 16
$2,500,000 X 0.53391 (PV of $1 due in 16 periods
at 4% from Table 3) ……………………………………………………. $1,334,775
Present value of interest to be received periodically
over the term of the bonds: $75,000* X 11.65230
(PV of $1 due each period for 16 periods at 4%
from Table 4) …………………………………………………………….. 873,923**
Present value of bonds and cash proceeds ……………………….. $2,208,698**
*($2,500,000 X .06 X 1/2) **Rounded
BRIEF EXERCISE A–17
i = 9%
? $3,200 $3,200 $3,200 $3,200 $3,200 $3,200 $3,200 $3,200
0 1 2 3 4 5 6 7 8
the retreading machine.