An interest paid only on the principal is called simple interest. When the interest of each period is added to the principal in computing the interest for the next period, it is called compound interest.

Interest amount computed at the end of a period is added to a single principal sum. That is, at the end of each interest period the interest earned for that period is added to the principal so that the interest also earns interest over the next interest period. In the same way, interest due on a debt at the end of a period is subject to interest in the next period.

Suppose that is deposited at a rate of interest per year. The amount on deposit at the end of the first year is found by the simple interest formula with t = 1;

(1)  

If the deposit earns compound interest, the interest earned during the second year is paid on the total amount on the deposit at the end of the first year. Using the formula again, with replaced by and t = 1, gives the total amount on deposit at the end of the second year;

(2)  

In the same way, the total amount on deposit at the end of the third year is;

(3)  

Generalizing, in t years the total amount on deposit is;

(4)  

called the compound amount.

3.1.1 The Formula  

The compound amount can be calculated using the following formula:

Compound amount:

(5)  

where i = r/m and n = mt ;

S = future (maturity) value, or the compound amount of P, or the accumulated value of P

P = original principal, or the present value of P, or the discounted value of S

i = interest rate per period

r = annual interest rate

m = number of compounding periods per year

n = number of compounding periods

t = number of years