Appendix B
Time Value of Money
QUICK STUDIES
Quick Study B-1 (10 minutes)
1.
2%
n = 8 periods
2.
12%
n = 2 periods
3.
3%
n = 4 periods
4.
1%
n = 24 periods
Quick Study B-2 (10 minutes)
In Table B.1, where n = 15 and p = $2,745/$10,000 = 0.2745, the i = 9%.
Quick Study B-3 (10 minutes)
In Table B.1, where i = 6% and p = $6,651/$10,000 = 0.6651, the n = 7.
Quick Study B-4 (10 minutes)
Quick Study B-5 (10 minutes)
Quick Study B-6 (10 minutes)
Quick Study B-7 (10 minutes)
Exercise B-1 (15 minutes)
Exercise B-2 (15 minutes)
Amount borrowed =
present value of $20,000 at 10% for 3 years
=
$20,000 x 0.7513 (using Table B.1, i = 10%, n = 3)
=
$15,026
Exercise B-3 (10 minutes)
Exercise B-4 (10 minutes)
Exercise B-5 (15 minutes)
10 years x 4 quarters = 40 interest periods
Exercise B-6 (15 minutes)
Exercise B-7 (10 minutes)
Exercise B-8 (10 minutes)
Exercise B-9 (10 minutes)
Interest rate per period = 12% annual / 12 months per year = 1% per month
Exercise B-10 (25 minutes)
1.
First Annuity
Future
Payment
Number of
Periods
Interest
Rate
Table B.1
Value
Amount
Borrowed
First payment ……..
$5,000
1
6%
0.9434
$ 4,717
Second payment …
5,000
2
6
0.8900
4,450
Third payment …….
5,000
3
6
0.8396
4,198
Fourth payment ….
5,000
4
6
0.7921
3,961
Fifth payment ……..
5,000
5
6
0.7473
3,737
Sixth payment …….
5,000
6
6
0.7050
3,525
Total borrowed …..
$24,588
Second Annuity
Future
Payment
Number of
Periods
Interest
Rate
Table B.1
Value
Amount
Borrowed
First payment ……..
$7,500
1
6%
0.9434
$ 7,076
Second payment …
7,500
2
6
0.8900
6,675
Third payment …….
7,500
3
6
0.8396
6,297
Fourth payment ….
7,500
4
6
0.7921
5,941
Total borrowed …..
$25,989
2.
First Annuity
Payment size …………………………….…..
$ 5,000
Number of payments ……………………..
6
Interest rate …………………………………..
6%
Value from Table B.3 ……………………..
4.9173
Present value of the annuity ……..…..
$24,587
(difference from part (1) due to rounding)
Second Annuity
Payment size …………………………….…..
$ 7,500
Number of payments ……………………..
4
Interest rate …………………………………..
6%
Value from Table B.3 ……………………..
3.4651
Present value of the annuity ……..…..
$25,988
(difference from part (1) due to rounding)
Exercise B-11 (30 minutes)
1. Present value of the annuity
Payment size …………………………….…..
$13,000
Number of payments ……………………..
4
Interest rate …………………………………..
4%
(semiannual)
Value from Table B.3 ……………………..
3.6299
Present value of the annuity ……..…..
$47,189
2. Present value of the annuity
Payment size …………………………….…..
$13,000
Number of payments ……………………..
4
Interest rate …………………………………..
6%
(semiannual)
Value from Table B.3 ……………………..
3.4651
Present value of the annuity ……..…..
$45,046
3. Present value of the annuity
Payment size …………………………….…..
$13,000
Number of payments ……………………..
4
Interest rate …………………………………..
8%
(semiannual)
Value from Table B.3 ……………………..
3.3121
Present value of the annuity ……..…..
$43,057
Exercise B-12 (15 minutes)
Semiannual interest payment = $500,000 x 10% x 1/2 = $25,000
Using Table B.1, where n = 30 and i = 4%, the p = 0.3083 (Principal payment)
Using Table B.3, where n = 30 and i = 4%, the p = 17.2920 (Interest payments)
0.3083 x $500,000 =
$154,150
present value of maturity amount
17.2920 x $ 25,000 =
432,300
present value of interest payments
$586,450
cash proceeds
Exercise B-13 (15 minutes)
Exercise B-14 (10 minutes)
Exercise B-15 (10 minutes)
Exercise B-16 (15 minutes)
12% annual / 12 months per year = 1% per month
2.5 years x 12 months per year = 30 total months
Exercise B-17 (15 minutes)
10 years x 4 quarters per year = 40 total quarters
12% annual / 4 quarters per year = 3% per quarter
In Table B.2, where n = 40 and i = 3%, the f = 3.2620.
In Table B.4, where n = 40 and i = 3%, the f = 75.4013.
Exercise B-18 (10 minutes)
a. p = present value of $60,000 at 9% for 4 years
p = $60,000 x 0.7084
p = $42,504
b. p = present value of $15,000 at 8% for 2 years
c. There are at least two ways to solve this problem. (1) We can take the
→The same answer results: choose $463 today
f = future value of $463 at 9% for 10 years
d. f = future value of $90 at 5% for 8 years
Exercise B-18 (concluded)
f. There are two aspects to this problem: a present value of a lump sum
part and a present value of an annuity part.
Part 1: p = present value of $10,000 at 6% for 10 years
Exercise B-19 (20 minutes)
a. (1) Present Value of a single amount.
(2) Multiply $10,000 by p from Table B.1.
(3) Use Table B.1, periods = 8 and interest rate = 4%.
OR