SIMPLE INTEREST AND COMPOUND INTEREST
Simple
Interest calculations refer to a type of interest calculation in which interest
earnings are calculated only on the principal (original) amount of the investment.
For
example, a $100 investment in a savings account earning 5% per year would grow
to $115.00 in three years.
|
Year # 1 |
|
|
Principal amount |
=
$100.00 |
|
Interest rate |
x
5.00% |
|
Interest earned |
= $5.00 |
|
|
|
|
Beginning amount |
=
$100.00 |
|
+ Interest earned |
+ $5.00 |
|
End of Year # 1 |
= $105.00 |
|
|
|
|
Year # 2 |
|
|
Principal amount |
=
$100.00 |
|
Interest rate |
x
5.00% |
|
Interest earned |
= $5.00 |
|
|
|
|
Beginning amount=
$100.00 |
|
|
+ Interest earned + $5.00 |
|
|
End of Year # 2= $105.00 |
|
|
|
|
|
Year # 3 |
|
|
Principal amount |
= $100.00 |
|
Interest rate |
x
5.00% |
|
Interest earned |
= $5.00 |
|
|
|
|
Beginning amount |
=
$100.00 |
|
+ Interest earned |
+ $5.00 |
|
End of Year # 3 |
= $105.00 |
In
each year only $5.00 in interest is earned. At
the end of year # 3, the investment has grown to only $115.00 by earning simple
interest of 5% per year on a $100 principal amount.
Compound Interest calculations refer to a type of interest calculation in which interest earnings are calculated not only on the principal (original) amount of the investment, but also on past interest earnings that are assumed to have been reinvested at the same rate. If the sum of money is invested for multiple years, interest paid is reinvested and future interest payments reflect interest earned on both the principal and the past interest earned.
For all types of interest bearing accounts and financial calculations, compound interest is the norm. Simple interest is rarely used today.
For
example, a $100 investment in a savings account earning 5% compound interest per year would grow
to $115.76 in three years.
|
Year # 1 |
|
|
Principal amount |
=
$100.00 |
|
Interest rate |
*
5.00% |
|
Interest earned |
= $5.00 |
|
|
|
|
Beginning amount |
=
$100.00 |
|
+ Interest earned |
+ $5.00 |
|
End of Year # 1 |
= $105.00 |
|
|
|
|
Year # 2 |
|
|
Beginning amount |
=
$105.00 |
|
Interest rate |
*
5.00% |
|
Interest earned |
= $5.25 |
|
|
|
|
Beginning amount |
=
$105.00 |
|
+ Interest earned |
+ $5.25 |
|
End of Year # 2 |
= $110.25 |
|
|
|
|
Year # 3 |
|
|
Beginning amount |
=
$110.25 |
|
Interest rate |
*
5.00% |
|
Interest earned |
= 5.5125 |
|
|
|
|
Beginning amount |
=
$110.25 |
|
+ Interest earned |
+
$5.5125 |
|
End of Year # 3 |
= $115.7625 |
or rounding off= $115.76
At
the end of year # 3, the investment has grown to approximately $115.76 by
earning 5% compound interest per year on a $100 principal (as opposed to the
$115 earned with simple interest).
These
calculations can be greatly simplified by the incorporation of interest rate
factors. An interest rate factor
for a single period is defined as (1+i)n
where i = the period’s percentage
interest rate stated as a decimal
and n is the number of periods compound interest is earned. In this case, the beginning amount earns compound interest for three years and the corresponding interest rate
factor is (1.05)3 or
(1.157625).
The
calculation now becomes;
|
Ending value |
Beginning value * 3 year interest rate factor |
|
Ending value |
= $100*(1.05)3 |
|
= 100*(1.157625) |
|
|
= $115.7625 |
or rounding to the penny gives us $115.76
This compound interest calculation provides us with a compound interest rate factor for 5% and n = 3.
This interest rate factor is also referred to as a Future Value Interest Factor (FVIF) since the future compound value is actually a future value.