The document discusses the time value of money concept that money today is worth more than money in the future. It defines simple and compound interest, and provides formulas to calculate interest and future value. For simple interest, interest is earned only on the principal amount. For compound interest, interest is earned on prior interest amounts as well as the principal. Examples are provided to demonstrate calculating interest and future value using simple and compound interest formulas.

2. The time value of money is the notion that a dollar today is worth
more than a dollar tomorrow.
SIMPLE INTEREST
Simple interest is interest earned on the principal amount. If the
amount of principal is unchanged from year to year, the interest per
year will remain the same. Interest can be calculated using the
following formula:
I = P X R X T
Where
I = Dollar amount of interest per year P = Principal R = Interest rate as a
percentage T = Time in years

3. Ex:
Assume that a firm has signed a two-year note payable for $3,000.
Interest and principal are to be paid at the due date with simple
interest at the rate of 10% per year.
I=P X R X T
=3000 X 0.10 X 2
= 600

4. Compound Interest
Compound interest means that interest is calculated on the principal plus
previous amounts of accumulated interest. Thus, interest is compounded, or
there is interest on interest.
A=P(1+r)t or FV=P(1+r)t or FV=PV(1+r)t
Where
PV= present value of investment or the principal investment amount
A/FV= the future value of the investment/loan, including interest
P= the principal investment amount
r= the annual interest rate (decimal)
t= the time the money is invested or borrowed for
1= Constant

5. Compound Interest
Ex: Assume a $3,000 note payable for which interest and principal are
due in two years with interest compounded annually at 10% per year.
Interest would be calculated as follows:
Sol. A=P(1+r)t A=3000(1+0.10)2
A=3,630
Year
1
2
Principal
Amount at
Interest
at 10%
Accumulated
at Year-End
3,000
$
3,300
$
300
$
330
$
3,300
$
3,630
$

6. Future value (FV)
• Refers to the amount of money an investment will grow to over some
period of time at some given interest rate.
• The amount an investment is worth after one or more periods.

7. Future Value with Simple Interest
Ex: 1. Suppose you invest $100 in a savings account that pays 10
percent interest per year. How much will you have in one year?
FV=PV+PV (r)(T)
FV=100+(100) (0.1)(1)
=110
Ex: 2. Going back to our $100 investment, what will you have after two
years, assuming the interest rate doesn’t change?
FV=100+(100)(0.1)(2)

8. Future Value with Compounding
Interest
Ex: Going back to our $100 investment, what will you have after two
years, assuming the interest rate is being reinvested and the interest
rate doesn’t change?
Sol. FV=PV(1+r)t
=100(1+0.1)2
=121

9. Future Value with Compounding
Interest
Ex: #2
Suppose that we want to find the future value of a $2,000 note payable
due in two years. The note payable requires interest to be compounded
quarterly at the rate of 12% per year.
Sol.
12%/4 quarters = 3% per quarter
FV= PV(1+r)t
= 2000(1+.03)8
=2000(1.267)
=$2, 534