Question

The difference between simple and compound interests compounded annually on a certain sum of money for $2$ years at $4\%$ per annum is $Re.1.$ Find the principal sum.

Answer 1

Let the sum $\left(P\right)$ be $Rs.x.$

Time, $T=2$ years

Rate, $R=4\%$

Difference between $C.I$ and $S.I=Re.1$

Compound Interest is given by the formula

$C.I=A-P$

$=P(1+\frac{R}{100}{)}^T-P$

$=x[1+\frac{4}{100}{]}^2-x]$

$=x\times [\frac{26}{25}{]}^2-x$

$=[\frac{676}{625}x-x]$

$=\frac{51}{625}x$

$S.I.=\frac{P\times R\times T}{100}=\frac{x\times 4\times 2}{100}$

$=\frac{2x}{25}$

$\therefore C.I-S.I=1$ [Given]

$\Rightarrow \frac{51x}{625}-\frac{2x}{25}=1$

$\Rightarrow \frac{51x}{625}-\frac{2x\times 25}{25\times 25}=1$

$\Rightarrow \frac{51x}{625}-\frac{50x}{625}=1$

$\Rightarrow \frac{51x-50x}{625}=1$

$\Rightarrow x=625$

Hence, the principal sum is $Rs.625.$