Question

The difference between the compound interest and simple interest on a certain sum at $15\%$ per annum for $3$ years is Rs. $283.50$.Find the sum.

Answer 1

Given: CI - SI $=Rs.283.50$

R $=15$ %

n $=3$ years

Let the sum be Rs. $x$

We know that : $A=P(1+\frac{R}{100}{)}^n$

$A=x(1+\frac{5}{100}{)}^3=x(1.05{)}^3\dots \dots$(i)

Aslo, $SI=\frac{P\times R\times n}{100}=\frac{x\times 15\times 3}{100}=0.45x\dots \dots$(ii)

Thus, we have :

CI - SI $=$ Rs. $283.50$

$x(1.05{)}^3-0.45x=283.50$ [from (i) & (ii)]

$\Rightarrow 1.157625x-0.45x=283.50$

$\Rightarrow 0.707625x=283.50$

$\Rightarrow x=\frac{283}{0.707625}=399.92934=400$

Thus, the sum is Rs $400$