The difference between the simple interest and the compound interest (compounded annually) on $Rs.1250$ for $2$ years at $8\%$ per annum will be?

Let $P$ be the principal amount

$r$ be the rate of interest, Then

Compound interest in two years is,

$C.I$ $=P(1+\frac{r}{100}{)}^2-P$ --(1)

Simple interest in $2$ years is,

$S.I$ $=\frac{2Pr}{100}$ ---(2)

Now, The difference between the simple interest and the compound interest (compounded annually),

$=C.P-S.P$

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

$=P\left(\right(1+\frac{r}{100}{)}^2-1-\frac{2r}{100})$

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

$=P{\left(\frac{r}{100}\right)}^2$

Difference of $S.I$ & $C.I$for $2$ years is $P{\left(\frac{r}{100}\right)}^2$

It is given that, $P=Rs.1250$ and $r=8\%$ and two years

Difference $=p{\left(\frac{r}{100}\right)}^2$

$=1250{\left(\frac{8}{100}\right)}^2$

$=1250{\left(\frac{2}{25}\right)}^2$

$=1250\times \frac{2}{25}\times \frac{2}{25}$

$=2\times 2\times 2$

$=8$

Hence, the required amount is $Rs.8$