Compound Interest – Quarterly compounding with fractional years: Find the amount on ₹ 15,000 at 12% per annum compounded quarterly for 1¼ years (i.e., 5 quarters).

Introduction / Context:
When compounding is quarterly, we convert the time into quarters and the rate into a quarterly rate. Fractional years are handled by counting exact compounding periods.

Given Data / Assumptions:

• P = ₹ 15,000
• Annual r = 12% → per quarter = 12%/4 = 3%
• Time = 1.25 years = 5 quarters

Concept / Approach:
Amount A = P * (1 + r/4)^(4t) = P * (1.03)^5.

Step-by-Step Solution:
A = 15000 * (1.03)^5(1.03)^5 ≈ 1.159274…A ≈ 15000 * 1.159274… = ₹ 17,389.12 (rounded to paise)

Verification / Alternative check:
Step compounding per quarter produces the same result within rounding tolerance.

Why Other Options Are Wrong:
Rs 16,596.88 and Rs 16,789.08 are too low; Rs 17,630.77 is too high for 5 quarters at 3%.

Common Pitfalls:
Using 1.25 as “quarters” directly, or applying 12% for 1.25 years without dividing by 4.

Final Answer:
Rs 17389.12