Question

A sum of money was invested for 3 years, interest being compounded annually. If the rates for successive years were 10% 15% and 18% respectively. if the compound interest for the second year amounted to rupees 4950, find the sum invested.

Answer 1

Suppose the sum of money invested is Rs.P

Rate of interest for first year = 10%

So amount accumulated for the first year; A1 = P(1+10/100)
= 11*P/10

Now rate of interest for the second year = 15%
So amount accumulated for the second year ; A2 = A1(1+15/100)
= 11P/10×23/20
= 253P/200

So compound interest for the second year A2−A1 = Rs.4950

253P/200−11P/10 = 4950

(253P−220P)200 = 4950

33P/200 = 4950

P = 4950×200/33 = 30000

Therefore sum of money invested was Rs.30000.