Question

A person invests Rs.$5000$ for three years at a certain rate of interest compounded annually. At the end of two years this sum amounts Rs.$6272$. Calculate :
(i) the rate of interest per annum.
(ii) the amount at the end of the third year

Answer 1

We have,

$A=Rs.6272,P=Rs.5000,T=2years$

Part $\left(i\right)$

We know that

$A=P{(1+\frac{R}{100})}^T$

or, $6272=5000{(1+\frac{R}{100})}^2$

or, ${(1+\frac{R}{100})}^2=1.2544$

or, $1+\frac{R}{100}=1.12$

or, $\frac{R}{100}=0.12$

or, $R=12\%$

Part $\left(ii\right)$

The amount at the end of the $3rd$ year.

$A=5000{(1+\frac{12}{100})}^3$

$A=5000{(1+\frac{3}{25})}^3$

$A=5000{\left(\frac{28}{25}\right)}^3$

$A=Rs.7024.64$