When the amount of interest earned at the end of the first period is added to the principal
(so both the principal and interest earns interest in the next period),
the interest is said to be compounded.
The sum of the original principal and total interest is called the compound amount or accumulated value.
(or future value or maturity value or S)
The amount of compound interest is the difference between the accumulated value S and the present value P.
Tools for Calculating Compound Interest
Number of periods (N) Number of years multiplied by the number of times the interest is compounded per year
For example, if you compounded $100 for 4 years at 8% annually, semiannually, or quarterly, what is N and R?
Number of periods (N) and Rate for each period (R)
Period
Rate
Annually: 4 × 1 = 4
Annually: 8% / 1 = 8%
Semiannually: 4 × 2 = 8
Semiannually: 8% / 2 = 4%
Quaterly: 4 × 4 = 16
Quaterly: 8% / 4 = 2%
Simple Versus Compound Interest
Let's look at the example below to illustrate the difference between simple and compound interest:
Simple Interest
Adam deposited $80 in a savings account for 4 years at an annual interest rate of 8%.
Question: What is Adam's simple interest and maturity value? Answer:
I = P × R × T = $80 × 0.08 × 4 = $25.60
MV = $80 + $25.60 = $105.60
Compound interest
Adam deposited $80 in a savings account for 4 years at an annual interest rate of 8%.
Question: What is Adam's interest and compounded amount?
See the below table that shows how to calculate the compound amount:
