Compound Interest – Find principal from 2-year amount at 4%: A sum amounts to ₹ 1,352 in 2 years at 4% compound interest (annual compounding). What was the principal?

Introduction / Context:
Finding the original principal from a known future amount over a fixed period at compound interest is a reverse-compounding problem. We divide the amount by the growth factor (1 + r)^t to retrieve the starting principal.

Given Data / Assumptions:

• A = 1,352
• r = 4% per annum
• t = 2 years
• Annual compounding

Concept / Approach:
Use P = A / (1 + r)^t = 1,352 / (1.04)^2. Calculate the denominator precisely to avoid rounding drift when comparing close options.

Step-by-Step Solution:
(1.04)^2 = 1.0816P = 1,352 / 1.0816 = 1,250

Verification / Alternative check:
Forward check: 1,250 * 1.0816 = 1,352, confirming the principal exactly.

Why Other Options Are Wrong:
₹ 1,200, ₹ 1,260, and ₹ 1,300 fail the exact reverse-compounding equality at 4% over 2 years. ₹ 1,180 is far from the required value.

Common Pitfalls:
Using simple interest to reverse compute principal will not match the compounded outcome; always divide by (1 + r)^t for CI problems.

Final Answer:
₹ 1,250