When the interest is calculated on the Principal for the entire period of loan, the interest is called simple interest and is given by
I = P × R × T
But if this interest is due (not paid) after the decided time period, then it becomes a part of the principal and so is added to the principal for the next time period, and the interest is calculated for the next time period on this new principal. Interest calculated, this way is called compound interest.
The time period after which the interest is added to the principal for the next time period is called the Conversion Period.
The conversion period may be one year, six months or three months and the interest is said to compounded, annually, semi-annually or quarterly.
Let a sum P be borrowed for n years at the rate of r% per annum, then
Interest for the first year = P × r/100 × 1 = Pr/100
Amount after one year = Principal for 2nd year = P + Pr/100 = P(1 + r/100)
Interest for 2nd year = P(1 + r/100) × r/100 × 1 = Pr/100 (1 + r/100)
Amount after n years
Compound Interest = A - P
Simple interest and compound interest are equal for first year (first conversion period).