B-1
Appendix B
Time Value of Money
QUICK STUDIES
Quick Study B-1 (10 minutes)
1.
12%
n = 2 periods
2.
n = 4 periods
3.
n = 8 periods
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-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)
Exercise B-3 (10 minutes)
Exercise B-4 (10 minutes)
B-3
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)
In Table B.3, where i = 10% and p = $82,014/$10,000 = 8.2014, the n = 18
(investor expects 18 annual payments to be received).
Exercise B-9 (10 minutes)
Interest rate per period = 12% annual / 12 months per year = 1% per month
B-4
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 …….
3
0.8396
Fourth payment ….
4
0.7921
Fifth payment ……..
5
0.7473
5,000
6
6
0.7050
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
2
0.8900
Third payment …….
7,500
3
6
0.8396
6,297
Fourth payment ….
4
0.7921
2.
First Annuity
Payment size …………………………………
$ 5,000
Number of payments ……………………..
6
Interest rate …………………………………..
Present value of the annuity ………….
$24,587
Payment size …………………………………
$ 7,500
Number of payments ……………………..
4
Interest rate …………………………………..
Present value of the annuity ………….
$25,988
Exercise B-11 (30 minutes)
1. Present value of the annuity
Payment size …………………………………
$13,000
Number of payments ……………………..
Interest rate …………………………………..
Value from Table B.3 ……………………..
Present value of the annuity ………….
$47,189
2. Present value of the annuity
Payment size …………………………………
$13,000
Number of payments ……………………..
Interest rate …………………………………..
Value from Table B.3 ……………………..
Present value of the annuity ………….
$45,046
3. Present value of the annuity
Payment size …………………………………
$13,000
Number of payments ……………………..
Interest rate …………………………………..
Value from Table B.3 ……………………..
Present value of the annuity ………….
$43,057
0.3083 x $500,000 =
17.2920 x $ 25,000 =
Exercise B-12 (15 minutes)
Semiannual interest payment = $500,000 x 10% x 1/2 = $25,000
Exercise B-13 (15 minutes)
1. $90,000 x 0.6651 (using Table B.1, i = 6%, n = 7) = $59,859.
Exercise B-14 (10 minutes)
In Table B.4, where n = 40 and f = $154,762/$1,000 = 154.762, the i = 6%
(investor must earn a 6% rate of interest).
Exercise B-15 (10 minutes)
Exercise B-16 (15 minutes)
12% annual / 12 months per year = 1% per month
Exercise B-17 (15 minutes)
10 years x 4 quarters per year = 40 total quarters
B-7
Exercise B-18 (10 minutes)
a. p = present value of $60,000 at 9% for 4 years
c. There are at least two ways to solve this problem. (1) We can take the
$463 today, compute its future value, and then compare it to the future
value amount of $1,000. (2) We can discount the $1,000 back to the
present and compare it to the $463 today.
d. f = future value of $90 at 5% for 8 years
e. f = future value of $158,500 at 10% 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
g. p = present value of $500,000 at 6% for 20 years
B-9
Exercise B-19 (20 minutes)
a. (1) Present Value of a single amount.
OR
(1) Future Value of a single amount.
b. (1) Future Value of an Annuity.
OR
(1) Present Value of an Annuity.
c. (1) Future Value of an Annuity.
d. (1) Present Value of an Annuity.
