Compound Interest – Find the principal from a 3-year amount: A sum amounts to ₹ 3,149.29 in 3 years at compound interest (compounded annually). What was the original principal?

Introduction / Context:
Back-calculating principal from a known compound amount is a standard inverse application of the compound interest formula. The question provides the final amount after 3 years, implying we can divide by the growth factor to retrieve the starting principal.

Given Data / Assumptions:

• Amount after 3 years, A = 3,149.29
• Compounded annually at some constant rate
• Answer choices suggest a common exam rate (e.g., 8%) that yields neat outcomes

Concept / Approach:
If the rate is 8% per annum, the 3-year factor is (1.08)^3 = 1.259712. Trying P = 2,500 gives A = 2,500 * 1.259712 ≈ 3,149.28/3,149.29, matching to cents/paise. Thus P = 2,500 is the consistent principal among the options.

Step-by-Step Solution:
Assume common exam rate r = 8% (validated by options)Compute factor: (1.08)^3 = 1.259712Trial with P = 2,500: A = 2,500 * 1.259712 = 3,149.28 ≈ 3,149.29Therefore, principal P = 2,500 fits perfectly within rounding.

Verification / Alternative check:
Reverse check: 3,149.29 / 2,500 = 1.259716 ≈ 1.259712 (rounding differences). No other option produces such a close exact power-of-1.08 match.

Why Other Options Are Wrong:
₹ 1,500, ₹ 2,000, or ₹ 3,000 would produce amounts far from 3,149.29 under standard small integer rates. ₹ 2,200 similarly fails the precise match with common rate powers.

Common Pitfalls:
Guessing a principal without checking a realistic rate can mislead. Always test whether a candidate principal times a plausible factor equals the given amount within minor rounding.

Final Answer:
₹ 2,500