The compound interest on a sum of $\text{₹}15800$ for $2$ years at $9\%$ per annum, when the interest is compounded $8$ -monthly, is (nearest to a rupee):

Given parameters:Principal ($P$) = $\text{₹}15800$ Time ($T$) = $2\text{ years}=24\text{ months}$ Rate ($R$) = $9\%\text{ per annum}$ Since compounding is done every $8$ months:
$$\text{Number of cycles }(n)=\frac{24\text{ months}}{8\text{ months}}=3$$
$$\text{Rate for 8 months }(R^{\prime })=9\%\times \frac{8}{12}=6\%$$
The total amount ($A$) after $3$ compounding periods is:
$$A=P{\left(1+\frac{R^{\prime }}{100}\right)}^n$$
$$A=15800\times {\left(1+\frac{6}{100}\right)}^3=15800\times (1.06{)}^3$$
Calculating $(1.06{)}^3$:
$$(1.06{)}^2=1.1236$$
$$(1.06{)}^3=1.1236\times 1.06=1.191016$$
Now, calculating the Amount ($A$):
$$A=15800\times 1.191016=18818.0528\approx \text{₹}18818$$
The Compound Interest (CI) is:
$$\text{CI}=A-P=18818-15800=\text{₹}3018$$