APPENDIX D
Time Value of Money
Learning Objectives
1. Distinguish between simple and compound interest.
2. Solve for future value of a single amount.
3. Solve for future value of an annuity.
4. Identify the variables fundamental to solving present value problems.
5. Solve for present value of a single amount.
6. Solve for present value of an annuity.
7. Compute the present value of notes and bonds.
8. Use a financial calculator to solve time value of money problems.
Summary of Questions by Learning Objectives and Bloom’s Taxonomy
Item LO BT Item LO BT Item LO BT Item LO BT Item LO BT
Brief Exercises
1. 2 AP 8. 5, 6 AP 14. 5, 6,
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE D-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 D-2
(a) (b) (a) (b)
(1) A 6% 3 periods (2) A 5% 8 periods
BRIEF EXERCISE D-3
FV = p X FV of 1 factor
BRIEF EXERCISE D-4
FV of an annuity of 1 = p X FV of an annuity factor
BRIEF EXERCISE D-5
FV = p X FV of 1 factor + (p X FV of an annuity factor)
= ($6,000 X 2.02582) + ($1,000 X 25.64541)
BRIEF EXERCISE D-6
FV = p X FV of 1 factor
BRIEF EXERCISE D-7
(a) (b)
(1) A 12% 6 periods
BRIEF EXERCISE D-8
(a) i = 10%
? $28,000
0 1 2 3 4 5 6 7 8 9
BRIEF EXERCISE D-8 (Continued)
(b) i = 9%
? $28,000 $28,000 $28,000 $28,000 $28,000 $28,000
0 1 2 3 4 5 6
BRIEF EXERCISE D-9
i = 9%
? $750,000
Discount rate from Table 3 is .64993 (5 periods at 9%). Present value of
BRIEF EXERCISE D-10
i = 10%
Discount rate from Table 3 is .46651 (8 periods at 10%). Present value of
BRIEF EXERCISE D-11
i = 5%
Discount rate from Table 4 is 10.37966. Present value of 15 payments of
BRIEF EXERCISE D-12
i = 8%
? $90,000 $90,000 $90,000 $90,000 $90,000 $90,000
0 1 2 3 4 5 6
BRIEF EXERCISE D-13
i = 4%
? $300,000
Diagram
for
Principal
0 1 2 3 4 19 20
Present value of principal to be received at maturity:
$300,000 X 0.45639 (PV of $1 due in 20 periods
at 4% from Table 3) ……………………………………………………… $136,917.00
BRIEF EXERCISE D-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:
$300,000 X .37689 (PV of $1 due in 20 periods
BRIEF EXERCISE D-15
i = 8%
? $64,000
Diagram
for
Principal
0 1 2 3 4 5 6
Present value of principal to be received at maturity:
$64,000 X .63017 (PV of $1 due in 6 periods
at 8% from Table 3) …………………………………………………….. $40,330.88
BRIEF EXERCISE D-16
i = 5%
? $2,600,000
Diagram
for
Principal
0 1 2 3 4 14 15 16
Present value of principal to be received at maturity:
$2,600,000 X 0.45811 (PV of $1 due in 16 periods
at 5% from Table 3) ……………………………………………………. $1,191,086*
BRIEF EXERCISE D-17
i = 10%
? $3,300 $3,300 $3,300 $3,300 $3,300 $3,300 $3,300 $3,300
0 1 2 3 4 5 6 7 8
BRIEF EXERCISE D-18
i = 4%
? $46,850 $46,850 $46,850 $46,850 $46,850 $46,850
0 1 2 3 4 9 10
BRIEF EXERCISE D-19
i = 10%
? $38,000 $40,000 $50,000
0 1 2 3
To determine the present value of the future cash flows, discount the future
cash flows at 10%, using Table 3.
BRIEF EXERCISE D-20
i = ?
$4,172.65 $10,000
0 1 2 3 4 14 15
BRIEF EXERCISE D-21
i = 10%
$25,490 $80,000
n = ?
Present value = Future value X Present value of 1 factor
BRIEF EXERCISE D-22
i = ?
? $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000
0 1 2 3 4 5 6 19 20
$9,128.55
BRIEF EXERCISE D-23
i = 11%
$1,000 $1,000 $1,000 $1,000 $1,000 $1,000
$5,146.12 n = ?
BRIEF EXERCISE D-24
10 ? –18,000 0 50,000
N I/YR. PV PMT FV
10.76%
BRIEF EXERCISE D-25
BRIEF EXERCISE D-26
BRIEF EXERCISE D-27
(a)
Inputs: 7 6.9 ? –16,000 0
N I PV PMT FV
(b)
Inputs: 10 8.65 ? 14,000 200,000
N I PV PMT FV
BRIEF EXERCISE D-28
(
a)
Note—set payments at 12 per year.
Inputs: 96 7.8 42,000 ? 0
N I PV PMT FV
A
(
b)
Note—set payments to 1 per year
.
Inputs: 5 7.25 8,000 ? 0
N I PV PMT FV
A