Question

A person invests Rs5,000 for three years at a certain rate of interest compounded annually. At the end of two years this sum amounts to Rs6,272. Calculate :
(i) the rate of interest per annum.
(ii) the amount at the end of the third year.

Answer 1

Given: P = Rs. 5,000; A = Rs. 6,272 and n = 2 years.

(i) ∴ `"A" = "P"( 1 + r/100)^n`

⇒ `6,272 = 5,000( 1 + r/100 )^2`

⇒ `6,272/5,000 = ( 1 + r/100 )^2`

⇒ `784/625 = ( 1 + r/100 )^2`

⇒ `(28/25)^2 = ( 1 + r/100 )^2`

On comparing,

`28/25 = 1 + r/100`

On solving, we get
r = 12%

(ii) Amount at the third year

= `5,000( 1 + 12/100 )^3`

= `5000(28/25)^3`

= Rs. 7,024.64