**Question:**

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?

**Solution:**

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