Question

On what sum of money will the difference between the simple interest and compound interest for $2$ years at $4\%$ per anum will be equal to$Rs.100$?

Answer 1

Let $P$ be the sum of money invested

Given : $R=4,T=2$

S.I. $=\frac{P\cdot T\cdot R}{100}$

$⟹S.I=\frac{P\times 2\times 4}{100}=\frac{2P}{25}$ ......... $\left(i\right)$

Now, $A=P{(1+\frac{4}{100})}^2$

C.I. $=A-P$

$=P{(1+\frac{4}{100})}^2-P$

$=P(1+\frac{16}{10000}+\frac{2\times 4}{100}-1)$

$=P(\frac{16}{10000}+\frac{800}{10000})$

$C.I.=P\left(\frac{816}{10000}\right)$ ........ $\left(ii\right)$

It is given that,

$|S.I.-C.I.|=100$

$⟹\frac{2P}{25}-P\left(\frac{816}{10000}\right)=100$

$⟹\frac{400P}{25\times 10000}=100$

$⟹P=62500$

Hence, the sum of money invested is Rs. $62,500$.