The simple interest in 3 years and the compound interest in 2 years on a certain sum at the same rate are Rs 1200 and Rs 832 respectively. Find the rate of inte

Question

Compound interest question

Answer 1

Let us assume that the interest is compounded annually for the compound interest case. Let the starting sum be S. For the simple interest case, the interest will be 3*I*s (I = interest rate as a fraction) after 3 years. 3*I*S = 1200 or I*S = 400.

For the compound interest case, the interest after 2 years is S*(1+I)^2 - S = 2*S*I + S*I^2 = 832. This implies that S*I^2 = 832 - 800 = 32, or that I = S*I^2/(S*I) = 32/400 = 8%. Therefore S = 400/0.08 = 5000. The initial principle is $5000 and the rate of interest is 8%.