Question

A person invests 5000 for 3 years at a certain rate of interest compounded annually. at the end of two years this amounts to 6272. calculate rate of interest per annum

Answer 1

A sum P, compounded annually will amount to A, which can be given by the formula,

A = P[1+r/100]^n, where r is the rate of interest and n is the compounding duration.

In this case, A = Rs. 6272, P = Rs. 5000, n = 2 and r needs to be found out.

Thus, 6272 = 5000[1+r/100]^2

or 6272/5000 = (1+r/100)^2

1+r/100 = sqrt (6272/5000) = sqrt (1.2544) = 1.12

Therefore, r/100 = 1.12-1 = 0.12

Or, the rate of interest is 12%.

The amount at the end of the third year is

A = 5000[1+12/100]^3 = 5000*1.404928 = Rs. 7024.64

Thus, the rate of interest, r = 12% and amount at the end of 3 years would be Rs. 7024.64