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-3 (10 minutes)
In Table B.1, where i = 6% and p = $6,651/$10,000 = 0.6651, the n = 7.
Quick Study B-7 (10 minutes)
In Table B.4, where n = 30 and i = 10%, the f = 164.494.
Ending value of the investment program: 164.494 x $1,500 = $246,741
EXERCISES
Exercise B-1 (15 minutes)
In Table B.1, where n = 6 and i = 10%, the p = 0.5645.
Present value of investment = $606,773 x .5645 = $342,523
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-5 (15 minutes)
10 years x 4 quarters = 40 interest periods
8% annual / 4 quarters per year = 2% per quarter
In Table B.2, where n = 40 and i = 2%, the f = 2.2080.
Total accumulation = 2.2080 x $7,200 = $15,897.60
Exercise B-6 (15 minutes)
In Table B.2, where n = 9 and i = 7%, the f = 1.8385.
Future value of investment = $163,170 x 1.8385 = $299,988
Exercise B-9 (10 minutes)
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
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
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
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)
Payment size …………………………………
$ 7,500
Interest rate …………………………………..
6%
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
0.3083 x $500,000 =
17.2920 x $ 25,000 =
Exercise B-13 (15 minutes)
1. $90,000 x 0.6651 (using Table B.1, i = 6%, n = 7) = $59,859.
2. $20,000 x 2.4869 (using Table B.3, i = 10%, n = 3) = $49,738.
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-16 (15 minutes)
12% annual / 12 months per year = 1% per month
2.5 years x 12 months per year = 30 total months
In Table B.4, where n = 30 and i = 1%, the f = 34.7849.
Total accumulation = 34.7849 x $50 = $1,739.25
Exercise B-17 (15 minutes)
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
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.
→The same answer results: choose $463 today
d. f = future value of $90 at 5% for 8 years
Formula: $90 = f x 0.6768; then solve for f
f = $90 / 0.6768
f = $132.98
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
p = $10,000 x 0.5584
p = $5,584
g. p = present value of $500,000 at 6% for 20 years
p = $500,000 x 11.4699
p = $5,734,950 (present value of real amount won)
Instructor note: It can be useful to extend this problem and assume a 30% tax rate. In this
case the annuity after-tax declines to $350,000. Accordingly, the present value of the after–
tax amount is $4,014,465. Again, nothing near the $10 million winnings advertised.
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
b. (1) Future Value of an Annuity.
(2) Divide $10,000 by f from Table B.4.
(3) Use Table B.4, periods = 8 and interest rate = 4%.
OR
c. (1) Future Value of an Annuity.
(2) Multiply $4,000 by f from Table B.4.
(3) Use Table B.4, periods = 40 and interest = 8%.
d. (1) Present Value of an Annuity.
(2) Multiply $30,000 by p from Table B.3.
