The compound interest on Rs 30,000 at 7% per annum is Rs 4,347 for a certain period. For how many years was the money invested at this rate?

Introduction:
This question asks you to determine the time period for a compound interest investment when the principal, rate, and total compound interest are known. Being able to reverse engineer time is very important in aptitude tests involving financial mathematics.

Given Data / Assumptions:

• Principal P = Rs 30,000
• Compound interest CI = Rs 4,347
• Annual interest rate r = 7% per annum
• Compounded annually
• We need to find number of years n

Concept / Approach:
First, compute the final amount A using:
A = P + CIThen apply the compound interest formula:
A = P * (1 + r)^nRearrange to get:
(1 + r)^n = A / PWe then look for n such that the power of (1 + r) matches this ratio. Often n turns out to be a small integer in exam problems.

Step-by-Step Solution:
Step 1: Compute the final amount.A = P + CI = 30,000 + 4,347 = Rs 34,347Step 2: Use the compound interest formula.A = P * (1 + r)^n34,347 = 30,000 * (1 + 0.07)^n34,347 = 30,000 * (1.07)^nStep 3: Form the ratio.(1.07)^n = 34,347 / 30,000(1.07)^n ≈ 1.1449Step 4: Compare powers of 1.07.(1.07)^1 = 1.07 (too small)(1.07)^2 = 1.1449 (exact match)Thus, n = 2 years.

Verification / Alternative check:
Let us verify by forward calculation for 2 years:
A = 30,000 * (1.07)^2 = 30,000 * 1.1449 = Rs 34,347CI = A - P = 34,347 - 30,000 = Rs 4,347Since this matches the given compound interest, the period is confirmed as 2 years.

Why Other Options Are Wrong:

• 3 years or more: (1.07)^3 and higher powers would give an amount significantly larger than Rs 34,347.
• 6 or 5 years: These would result in a much higher factor than 1.1449, creating a much bigger compound interest than Rs 4,347.

Common Pitfalls:
Some students try to assume simple interest and use linear relationships, which does not work for compound interest. Others do not compute the ratio correctly, or they round intermediate values too aggressively, leading to a wrong n. Always calculate A / P carefully and compare with standard powers of (1 + r).

Final Answer:
The money was invested for 2 years at 7% compound interest per annum.