The compound interest on a sum of ₹ $24500$ at $10\%$ p.a for $2\frac{2}{5}$ years interest compounded yearly is:

Given:Principal, $P=\text{₹ }24500$ Rate, $R=10\%$ p.a.Time $=2\frac{2}{5}$ yearsFor the first 2 years, the rate is $10\%$ per year.For the remaining $\frac{2}{5}$ year, the effective rate is:
$$R^{\prime }=\frac{2}{5}\times 10\%=4\%$$
The total amount $A$ after $2\frac{2}{5}$ years is:
$$A=P\times {\left(1+\frac{10}{100}\right)}^2\times \left(1+\frac{4}{100}\right)$$
$$A=24500\times (1.1{)}^2\times (1.04)$$
$$A=24500\times 1.21\times 1.04$$
$$A=29645\times 1.04=30830.80$$
Compound Interest ($\text{CI}$):
$$\text{CI}=A-P=30830.80-24500=\text{₹ }6330.80$$