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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

1. $625$
2. $630$
3. $640$
4. $650$

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

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