**Question:**

Neha borrowed Rs 24000 from the State Bank of India to buy a scooter. If the rate of interest be 10% per annum compounded annually, what payment will she have to make after 2 years 3 months?

**Solution:**

Principal amount, $P=$ Rs. 24000

Rate of interest, $R=10 \%$ p. a.

Time, $n=2$ years 3 months $=2 \frac{1}{4}$ years

The formula for the amount including the compound interest is given below:

$\mathrm{A}=P \times\left(1+\frac{R}{100}\right)^{n} \times\left(1+\frac{\frac{1}{4} R}{100}\right)$

$=$ Rs. $24000 \times\left(1+\frac{10}{100}\right)^{2} \times\left(1+\frac{\frac{1}{4} \times 10}{100}\right)$

$=$ Rs. $24000 \times\left(\frac{100+10}{100}\right)^{2} \times\left(\frac{100+2.5}{100}\right)$

$=$ Rs. $24000 \times\left(\frac{110}{100}\right)^{2} \times\left(\frac{100+2.5}{100}\right)$

$=$ Rs. $24000 \times(1.1 \times 1.1 \times 1.025)$

$=$ Rs. $24000 \times(1.250)$

$=$ Rs. 29766

Therefore, Neha should pay Rs 29766 to the bank after 2 years 3 months.