The compound interest on Rs. 30,000 at 7% per annum amounts to Rs. 4,347. For how many years was the money invested at this rate of compound interest, assuming annual compounding?

Introduction:
Here we are given a principal, a rate of compound interest, and the total compound interest earned. Instead of finding the interest, we are required to determine the time period for which the money must have been invested at the given rate to generate the specified compound interest.

Given Data / Assumptions:

• Principal (P) = Rs. 30,000
• Rate (r) = 7% per annum
• Compound interest (CI) = Rs. 4,347
• Interest is compounded annually

Concept / Approach:
The compound amount after t years is:
A = P * (1 + r/100)^tThe compound interest is:
CI = A - PSo we can write:
CI = P * (1 + r/100)^t - P = P * [(1 + r/100)^t - 1]We know CI, P, and r, so we solve for t by isolating the term (1 + r/100)^t.

Step-by-Step Solution:
Step 1: Substitute the known values: 4,347 = 30,000 * [(1 + 7/100)^t - 1].Step 2: Convert the rate: 1 + 7/100 = 1.07.Step 3: Divide both sides by 30,000: 4,347 / 30,000 = (1.07)^t - 1.Step 4: Compute the fraction: 4,347 / 30,000 = 0.1449.Step 5: So (1.07)^t - 1 = 0.1449, therefore (1.07)^t = 1.1449.Step 6: Compare with powers of 1.07. We know (1.07)^2 = 1.07 * 1.07 = 1.1449.Step 7: Therefore t = 2 years.The money was invested for exactly 2 years.

Verification / Alternative check:
Verify by computing the amount for 2 years directly: A = 30,000 * (1.07)^2 = 30,000 * 1.1449 = 34,347. Compound interest = 34,347 - 30,000 = 4,347, which matches the given CI, confirming that the period is 2 years.

Why Other Options Are Wrong:
For t = 1 year, CI would be only 7% of 30,000, that is Rs. 2,100, which is too small. For t = 3, 4, or 5 years, the interest accumulated would be much larger than Rs. 4,347 due to repeated compounding, so these options cannot be correct. The option of 1 year is also inconsistent with the given CI value.

Common Pitfalls:
Students may try to treat the problem using simple interest or by guessing the time period without checking powers of (1 + r/100). Others may make errors when dividing CI by the principal or neglect the minus one in the expression (1.07)^t - 1. Carefully manipulating the formula and checking plausible integer values of t is a reliable approach.

Final Answer:
The money must have been invested for 2 years at 7% per annum compound interest to earn Rs. 4,347 as compound interest.