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

Option A. 625

Let the sum be Rs. x. Then,

C.I. = x$\left ( 1 + \frac{4}{100} \right )^{2}$ – x = $\frac{51}{625}$x

S.I. = $\frac{x * 4 * 2}{100}$ = $\frac{2}{25}$x

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

$\Rightarrow$ x = 625

Answer is A

If the difference between compound and simple interest is of two years then, direct formula can be applied.

$Difference =Principal(1+\frac{Rate}{100})^{2}$

Rs.1 $=P*(\frac{4}{100})^{2}$

P = Rs.625

Difference between simple and compound interests is of 3 years = $3P(\frac{R}{100})^{2}+P(\frac{R}{100})^{3}$

Above formulae can be used only if the difference between CI and SI are 2 years and 3 years.