Question

The difference between S.I. and C.I. at $12\%$ per annum for $6$ years on a certain sum is $500$. Find the sum.

• A. $1976.28$
• B. $2976.28$
• C. $3976.28$
• D. $4976.28$

Answer 1

The correct option is A $1976.28$

Compound interest $=$ Amount $-$ Principal
$\text{C.I.}=P{(1+\frac{R}{100})}^n-P=P[1+\frac{12}{100}{]}^6-1]$
$\text{C.I.}=0.973P$
Simple interest, S.I. $=$ $\frac{\text{PNR}}{100}$
$\text{S.I.}=\frac{P\times 12\times 6}{100}$
S.I. $=0.72P$
Now C.I. $-$ S.I. $=500$
$\Rightarrow 0.973P-0.72P=500$
$\Rightarrow P=\frac{500}{0.253}$
$\Rightarrow P=$ Rs.$1976.28$