Half-yearly compounding for 1.5 years at 10% nominal: What is the compound interest on ₹ 8000 at 10% per annum for 1.5 years when interest is compounded half-yearly?

Introduction / Context:When interest is credited more frequently than yearly, use the periodic rate and number of periods. For half-yearly compounding, divide the nominal annual rate by 2 and multiply years by 2 to get the number of half-years.

Given Data / Assumptions:

• P = ₹ 8000
• Nominal r = 10% p.a.; half-yearly rate = 10%/2 = 5%
• Time = 1.5 years → n = 3 half-years

Concept / Approach:Amount A = P * (1 + i)^n, where i = 0.05 and n = 3. Then CI = A − P.

Step-by-Step Solution:A = 8000 * (1.05)^3 = 8000 * 1.157625 = ₹ 9261CI = 9261 − 8000 = ₹ 1261

Verification / Alternative check:Effective 1.5-year multiplier at 10% nominal, half-yearly: (1.05)^3 = 1.157625, so a 15.7625% gain on ₹ 8000 is ₹ 1261 (rounded to whole rupees here exact).

Why Other Options Are Wrong:₹ 1385 and ₹ 1480 assume higher periodic rates or counts; ₹ 1255 is slightly low; ₹ 1200 ignores compounding beyond simple 15%.

Common Pitfalls:Using 1.10^(1.5) (annual compounding) instead of half-yearly periods; forgetting that 1.5 years equals 3 half-years.

Final Answer:₹ 1261