Step 1: Compound Interest Formula.
The compound interest formula is:
\[A = P \left( 1 + \frac{r}{n} \right)^{nt}\]
where \(P = 15000\), \(r = 8%\), \(t = \frac{3}{2} \, \text{years}\), and \(n\) represents the number of compounding periods.
Step 2: Case 1 - Compounded Semi-Annually.
With semi-annual compounding, \(n = 2\). The formula yields:
\[A = 15000 \left( 1 + \frac{8}{2 \times 100} \right)^{2 \times \frac{3}{2}} = 15000 \left( 1 + 0.04 \right)^{3} = 15000 \times 1.04^3\]
Calculating \(1.04^3\):
\[A \approx 15000 \times 1.124864 = 16872.96\]
The compound interest is:
\[CI_{\text{semi}} = 16872.96 - 15000 = 1872.96 \approx 1873\]
Step 3: Case 2 - Compounded Annually.
For annual compounding, \(n = 1\). The formula becomes:
\[A = 15000 \left( 1 + \frac{8}{100} \right)^{\frac{3}{2}} = 15000 \times 1.08^{1.5}\]
Calculating \(1.08^{1.5}\):
\[A \approx 15000 \times 1.121032 = 16815.48\]
The compound interest is:
\[CI_{\text{annual}} = 16815.48 - 15000 = 1815.48 \approx 1815\]
Step 4: Difference in Interest.
The difference in compound interest is:
\[CI_{\text{semi}} - CI_{\text{annual}} = 1873 - 1815 = 58\]
The difference is ₹58.
Final Answer: \[\boxed{20}\]