Compound Interest — Find the compound interest on Rs. 2800 for 1.5 years at 10% p.a. (annual compounding; last half-year taken as simple on the amount after 1 year).

Introduction / Context:
When time is fractional and compounding is annual, compute full-year compounding first, then apply simple interest for the remaining fraction on the amount after the last full year.

Given Data / Assumptions:

• P = Rs. 2800.
• r = 10% p.a.
• t = 1.5 years; annual compounding with last 0.5 year at simple on the 1-year amount.

Concept / Approach:
Amount after 1 year: A1 = P * (1 + r) = 2800 * 1.10. For the next 0.5 year: add A1 * r * 0.5. The compound interest is final amount minus principal.

Step-by-Step Solution:
A1 = 2800 * 1.10 = 3080.Extra for 0.5 year = 3080 * 0.10 * 0.5 = 154.Final amount = 3080 + 154 = 3234.Compound interest = 3234 − 2800 = Rs. 434.

Verification / Alternative check:
Equivalent factor: 1.10 * 1.05 = 1.155; 2800 * 1.155 = 3234; CI = 434.

Why Other Options Are Wrong:
They correspond to misapplied rates, compounding, or using SI for the whole interval.

Common Pitfalls:
Compounding the half-year on the principal instead of on A1, or mistakenly compounding semi-annually.

Final Answer:
Rs. 434