Question

$\text{Rs.}12,500$ lent at compound Interest for two years at $10\%$ per annum fetches $\text{Rs.}$ ____ more, if the interest was payable half yearly than if it was payable annually -

• A. $0$
• B. $\text{Rs.}10.48$
• C. $\text{Rs.}38.50$
• D. $\text{Rs.}68.82$

Answer 1

The correct option is D $\text{Rs.}68.82$

$P=\text{Rs.}12,500$

$R=10\%$

$T=2$ years

If interest is payable Annually

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

$=12,500{(1+\frac{10}{100})}^2$

$=\text{Rs.}15125$

$\therefore I=A-P$

$=(15125-12500)$

$=\text{Rs.}2625$

If interest is payable semi-annually.

$A=P{(1+\frac{R}{200})}^{2T}$

$=12500{(1+\frac{10}{200})}^{2\times 2}$

$=\text{Rs.}15193.8$

$\therefore I=A-P$

$=15193.8-12500$

$=\text{Rs.}2693.8$

$\therefore$ Extra Interest fetched $=\text{Rs.}(2693.8-2625)$

$=\text{Rs.}68.82$