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APPENDIX G
Time Value of Money
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE G-1
(a) Interest = p X i X n
(b) Future value factor for 12 periods at 5% is 1.79586 (from Table 1)
BRIEF EXERCISE G-2
(1) Case A 5% 3 periods (2) Case A 3% 8 periods
Case B 6% 8 periods Case B 4% 12 periods
BRIEF EXERCISE G-3
FV = p X FV of 1 factor
BRIEF EXERCISE G-4
FV of an annuity of 1 = p X FV of an annuity factor
BRIEF EXERCISE G-5
FV = p X FV of 1 factor + (p X FV of an annuity factor)
BRIEF EXERCISE G-6
FV = p X FV of 1 factor
BRIEF EXERCISE G-7
(a) (b)
(1) 12% 7 periods
BRIEF EXERCISE G-8
BRIEF EXERCISE G-8 (Continued)
(b) i = 9%
0 1 2 3 4 5 6
Discount rate from Table 4 is 4.48592 (6 periods at 9%). Present value of
BRIEF EXERCISE G-9
0 1 2 3 4 5 6
Discount rate from Table 3 is .63017 (6 periods at 8%). Present value of
$750,000 to be received in 6 years discounted at 8% is therefore $472,627.50
BRIEF EXERCISE G-10
BRIEF EXERCISE G-11
0 1 2 3 4 14 15
Discount rate from Table 4 is 8.55948. Present value of 15 payments of
BRIEF EXERCISE G-12
0 1 2 3 4 5 6
Discount rate from Table 4 is 5.07569. Present value of 6 payments of $80,000
BRIEF EXERCISE G-13
Diagram
for
Principal
0 1 2 3 4 19 20
Diagram
for
Interest
0 1 2 3 4 19 20
Present value of principal to be received at maturity:
Present value of interest to be received periodically
BRIEF EXERCISE G-14
The bonds will sell at a discount (for less than $300,000). This may be proven
as follows:
Present value of principal to be received at maturity:
Present value of interest to be received periodically
(PV of $1 due each period for 20 periods at 6%
*Rounded.
BRIEF EXERCISE G-15
Diagram
for
Principal
0 1 2 3 4 5 6
Diagram
for
Interest
0 1 2 3 4 5 6
$65,000 X .70496 (PV of $1 due in 6 periods
BRIEF EXERCISE G-16
Diagram
for
Principal
0 1 2 3 4 14 15 16
Diagram
for
Interest
0 1 2 3 4 14 15 16
Present value of principal to be received at maturity:
$2,500,000 X 0.53391 (PV of $1 due in 16 periods
BRIEF EXERCISE G-17
0 1 2 3 4 5 6 7 8
Discount rate from Table 4 is 5.53482. Present value of 8 payments of $3,200
