Simple interest is based on the principal amount of a loan or deposit, which remains constant while calculating it against the interest rate, which is a percentage of the principal amount of the loan.
Compound interest is based on the principal amount plus the interest that accumulates on it in every period, i.e. at the end of each period, the amount on which the interest rate is applied increases.

Formulae
Illustration of Calculation

 Simple Interest Compound interest Period 1 – Interest rate 10% Principal amount Kshs 100,000/   Interest = 100,000 x 10% = 10,000   Debt at end of period Kshs 110,000 Period 1 – Interest rate 10% Principal amount Kshs 100,000/   Interest = 100,000 x 10% = 10,000   Debt at end of period Kshs 110,000 Period 2 – Interest rate 10% Principal amount Kshs 100,000/   Interest = 100,000 x 10% = 10,000   Debt at end of period if period 1 interest not paid = 110,000+10,000 = 120,000 Period 2 – Interest rate 10% Principal amount Kshs 110,000/=   Interest = 110,000 x 10% = 11,000   Debt at end of period if period 1 interest not paid = 110,000+11,000 = 121,000 Period 3 – Interest rate 10% Principal amount Kshs 100,000/ Interest = 100,000 x 10% = 10,000   Debt at end of period if period 1 & 2 interest not paid = 120,000+10,000 = 130,000 Period 3 – Interest rate 10% Principal amount Kshs 121,000/=   Interest = 121,000 x 10% = 12,00 Debt at end of period if period 1 & 2 interest not paid = 121,000+12,100 = 133,100 Period 4 – Interest rate 10% Principal amount Kshs 100,000/   Interest = 100,000 x 10% = 10,000 Debt at end of period if period 1, 2 & 3 interest not paid = 130,000+10,000 = 140,000 Period 3 – Interest rate 10% Principal amount Kshs 133,100/=   Interest = 133,100 x 10% = 13,310 Debt at end of period if period 1, 2 & 3 interest not paid = 133,100+13,310 = 146,410