Appendix B
Time Value of Money
QUICK STUDIES
Quick Study B-1 (10 minutes)
1. 2% n = 8 periods
2. 12% n = 2 periods
Quick Study B-2 (10 minutes)
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)
In Table B.2, where n = 10 and i = 12%, the f = 3.1058.
Quick Study B-6 (10 minutes)
In Table B.3, where n = 6 and i = 7%, the p = 4.7665.
Quick Study B-7 (10 minutes)
In Table B.4, where n = 30 and i = 10%, the f = 164.494.
EXERCISES
Exercise B-1 (15 minutes)
Exercise B-2 (15 minutes)
Exercise B-3 (10 minutes)
In Table B.2, where i = 12% and f = $96,463/$10,000 = 9.6463, the n = 20
(implies the investor must wait 20 years before payment).
Exercise B-4 (10 minutes)
Exercise B-5 (15 minutes)
10 years x 4 quarters = 40 interest periods
Exercise B-6 (15 minutes)
In Table B.2, where n = 9 and i = 7%, the f = 1.8385.
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
Using Table B.3, where n = 40 and i = 1%, the p = 32.8347. This means:
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
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
2.
First Annuity
Payment size………………………………… $ 5,000
Number of payments…………………….. 6
Interest rate………………………….………. 6%
Second Annuity
Payment size………………………………… $ 7,500
Number of payments…………………….. 4
Interest rate………………………….………. 6%
Exercise B-11 (30 minutes)
1. Present value of the annuity
Payment size………………………………… $13,000
Number of payments…………………….. 4
2. Present value of the annuity
Payment size………………………………… $13,000
Number of payments…………………….. 4
Interest rate………………………….………. 6% (semiannual)
3. Present value of the annuity
Payment size………………………………… $13,000
Number of payments…………………….. 4
Interest rate………………………….………. 8% (semiannual)
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)
Exercise B-13 (15 minutes)
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
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
Exercise B-18 (10 minutes)
a. p = present value of $60,000 at 9% for 4 years
b. p = present value of $15,000 at 8% for 2 years
p = $15,000 x 0.8573
p = $12,859.50
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
p = present value of $1,000 at 9% for 10 years
p = $1,000 x 0.4224
p = $422.40 (which is less than $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 2: p = present value of $400 annuity at 6% for 10 years
p = $400 x 7.3601
p = $2,944
$8,528 = $5,584 + $2,944 (we are willing to pay $8,528 for this investment)
g. p = present value of $500,000 at 6% for 20 years
p = $500,000 x 11.4699
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%.