Compound Interest – Half-yearly compounding in one year: Raja invests ₹ 15,000 at 10% per annum, compounded half-yearly. What is the amount at the end of 1 year?

Introduction / Context:
With half-yearly compounding, the annual rate is split into two periods. Each half-year applies r/2, and there are 2 periods in one full year.

Given Data / Assumptions:

• P = ₹ 15,000
• Nominal annual rate = 10%
• Compounding = semiannual → rate per period = 10%/2 = 5%
• Number of periods in 1 year = 2

Concept / Approach:
Amount A = P * (1 + r/m)^(m*t), where m = 2 for half-yearly.

Step-by-Step Solution:
A = 15000 * (1 + 0.10/2)^(2*1)A = 15000 * (1.05)^2 = 15000 * 1.1025A = ₹ 16,537.50

Verification / Alternative check:
Sequential: After 6 months = 15000 * 1.05 = 15750; after 12 months = 15750 * 1.05 = 16537.50.

Why Other Options Are Wrong:
₹ 18,000, ₹ 19,000.50, and ₹ 20,000 assume larger rates or extra periods.

Common Pitfalls:
Applying 10% once (simple interest) or missing the second compounding within the year.

Final Answer:
₹ 16537.50