CHAPTER 1 MODULE 1
Time Value
of Money Module 1
Introduction to Accounting I
Professor Marc Smith
Time Value of Money – Module 1
Measurement and recording of liabilities are
based on the concept of the time value of
money.
Time Value of Money = Compound Interest
Time Value of Money – Module 1
Compound Interest
v.
Simple Interest
Simple Interest:
P x R x T
Earns interest on the principal invested.
Compound Interest:
Earns interest on both principal invested
as well as all previously earned interest.
Time Value of Money – Module 1
Four Time Value of Money Cases
1. Future Value of a Lump Sum
2. Present Value of a Lump Sum
3. Future Value of an Annuity
4. Present Value of an Annuity
Time Value of Money – Module 1
In each of the four time value of money cases, you will need
to make use of table factors. These table factors can be
found on the course website. Please print the table factors
from the website and have them available as you work
through the modules for this chapter.
If you look at the table factors, you will see that you need to
know two variables in order to determine the correct factor to
use. You need to know the number of periods (n) and the
interest rate (i).
The n is located in the left column of each table and the i can
be found in the row at the top of each table. The intersection
of the i and n is the table factor you will use to solve your
problem.
Time Value of Money – Module 1
In the future value of a lump sum case, we know the value
of some amount today and we want to know the value at
some point in the future.
•How much will today’s dollar be worth in the future?
Future Value = Present Value x Future Value Factor i,n
?
TODAY
FUTURE
Time Value of Money – Module 1
Periods
5%
4
1.2155
5
1.2783
8
1.4775
10
1.6289
6%
1.2625
1.3382
1.5939
1.7909
8%
1.3605
1.4693
1.8510
2.1589
10%
1.4641
1.6105
2.1436
2.5938
Future Value = Present Value x FV Factor
10% | 5
Future Value = $10,000 x 1.6105
Future Value = $16,105
How much interest will Sandy
earn over the five years?
$6,105
($16,105 - $10,000)
Time Value of Money – Module 1
Question:
What happened in part (a) that
made our calculations easier?
Answer:
The interest was compounded
annually.
Compounding — the frequency with which interest
is added to the principal.
When interest is compounded in any way other
than annually, you must make adjustments to the
interest rate (i) and the time period (n).
Time Value of Money – Module 1
Necessary adjustments to i & n
i
÷
n
x
NOTE:
# of compounds per year
# of compounds per year
These adjustments must be made in all
time value of money cases.
Time Value of Money – Module 1
Periods
5%
4
1.2155
5
1.2783
8
1.4775
10
1.6289
6%
1.2625
1.3382
1.5939
1.7909
8%
1.3605
1.4693
1.8510
2.1589
10%
1.4641
1.6105
2.1436
2.5938
Future Value = Present Value x FV Factor 5% | 10
Future Value = $10,000 x 1.6289
Future Value = $16,289
How much interest will Sandy
earn over the five year?
$6,289
($16,289 - $10,000)
Time Value of Money – Module 1
Periods
5%
4
1.2155
5
1.2783
8
1.4775
10
1.6289
6%
1.2625
1.3382
1.5939
1.7909
8%
1.3605
1.4693
1.8510
2.1589
10%
1.4641
1.6105
2.1436
2.5938
Future value factors can be calculated as follows:
(1 + i)
n
Thus, the future value factor at 5% and 10 periods:
(1 + .05)
10
= (1.05)
10
= 1.628895
In answering quiz and exam question, always use the
table factors provided.
Time Value of Money – Module 1
Question:
As the compounding frequency increases,
what happened to the future value?
Answer:
It increases.
FV Annual Compounding
FV Semi-Annual Compounding
$16,105
$16,289
Question:
Why does this happen?
Answer:
The more frequent the compounding, the
more interest is earned on interest thus
giving a higher future value.