Question

The difference between the C.I. and S.I. on a sum of money deposited for $4$ years at $5\%$ per annum was Rs. $15$. Find the sum of the money.

• A. $667.74$
• B. $767.74$
• C. $867.74$
• D. $967.74$

Answer 1

The correct option is D $967.74$

Compound interest $=$ Amount $-$ Principal
$\text{C.I.}=P{(1+\frac{R}{100})}^n-P=P[{[1+\frac{5}{100}]}^4-1]$
$\text{C.I.}=0.2155P$
Simple interest, S.I. $=$ $\frac{\text{PNR}}{100}$
$\text{S.I.}=\frac{P\times 5\times 4}{100}$
$\text{S.I.}=0.2P$
Now C.I. $-$ S.I. $=15$
$\Rightarrow 0.2155P-0.2P=15$
$\Rightarrow P=\frac{15}{0.0155}$
$\Rightarrow P=$ Rs. $967.74$