Question

On what sum of money does the difference between the simple interest and compound interest in $2$ years at $5\%$ is $Rs.15$

Answer 1

Let the sum of money $=x$

Simple interest in $2$ years $=\frac{P\times R\times T}{100}$

where $P=$ Principal $=x$, Rate, $R=5\%$ and Time, $T=2$ years

so Simple Interest $=\frac{x\times 5\times 2}{100}=0.1x$

Compound interest:

Amount after $1$ year $=x+5\%$ of $x=1.05x$

Amount after $2$ years $=1.05x+5\%\left(1.05x\right)=1.05x+0.0525x=1.1025x$

So compound interest after $2$ years $=1.1025x-x=0.1025x$

Difference of compound interest and simple interest $=0.1025x-0.1x=0.0025x$

This difference in interest is given as $Rs.15$.

So $0.0025x=15$

$\Rightarrow x=\frac{15}{0.0025}=Rs.6000$

Hence, the sum is $Rs.6000$