The simple interest on a sum of money for 2 years at 8% per annum is Rs 2400. What will be the compound interest on that sum at the same rate and for the same period?
Simple interest $(\mathrm{SI})=$ Rs. 2400
Rate of interest, $R=8 \%$
Time, $n=2$ years
The principal can be calculated using the formula:
$\operatorname{Sum}=\left(\frac{100 \times \mathrm{SI}}{\mathrm{R} \times \mathrm{T}}\right)$
$\Rightarrow$ Sum $=$ Rs. $\left(\frac{100 \times 2400}{8 \times 2}\right)=$ Rs. 15000
i.e., the principal is Rs. 15000 .
The amount including the compound interest is calculated using the formula given below:
$\mathrm{A}=P\left(1+\frac{R}{100}\right)^{n}$
$=$ Rs. $15000\left(1+\frac{8}{100}\right)^{2}$
$=$ Rs. $15000\left(\frac{100+8}{100}\right)^{2}$
$=$ Rs. $15000\left(\frac{108}{100}\right)^{2}$
$=$ Rs. $15000(1.08 \times 1.08)$
$=$ Rs. 17496
i.e., the amount including the compound interest is Rs. 17496 .
$\therefore$ Compound interest $(\mathrm{CI})=$ Rs. $(17496-15000)=$ Rs. 2496