The compound interest on Rs. 30,000 at 7% per annum, compounded annually, is Rs. 4,347. For how many complete years was the money invested?

Introduction:
In this question we are given the principal, the interest rate, and the total compound interest earned. We are asked for the time period in years. This is a reverse compound interest problem where we solve for the number of years n such that the compound interest on 30,000 rupees at 7% per annum equals 4,347 rupees.

Given Data / Assumptions:

• Principal, P = Rs. 30,000
• Compound interest, CI = Rs. 4,347
• Annual interest rate, r = 7% per annum
• Compounding frequency: annually
• Number of years, n, is an integer we need to find

Concept / Approach:
The total amount A after n years at compound interest is: A = P * (1 + r / 100)^n The compound interest is: CI = A - P We know CI and P, so: A = P + CI = 30000 + 4347 = 34347 We then solve: 30000 * (1 + 0.07)^n = 34347

Step-by-Step Solution:
Step 1: Compute the total amount A. A = P + CI = 30000 + 4347 = 34347 rupees Step 2: Write the compound amount equation. 34347 = 30000 * (1.07)^n Step 3: Divide both sides by 30000. (1.07)^n = 34347 / 30000 ≈ 1.1449 Step 4: Check n by trial for small integers. For n = 1: (1.07)^1 = 1.07, which is too small. For n = 2: (1.07)^2 = 1.1449 exactly (rounded). Step 5: Since (1.07)^2 gives the required factor, n = 2.

Verification / Alternative check:
We can verify by directly computing the compound interest for n = 2 years. A = 30000 * (1.07)^2 = 30000 * 1.1449 = 34347 CI = A - P = 34347 - 30000 = 4347 This matches the given compound interest, confirming that the investment duration is indeed 2 years.

Why Other Options Are Wrong:
1 year: For one year, the interest would be 30000 * 0.07 = 2100, which is far less than 4347. 3 years: (1.07)^3 ≈ 1.225043, giving A ≈ 30000 * 1.225043 ≈ 36751, which leads to CI around 6751, not 4347. 4 years and 5 years: These would produce even larger amounts and much higher compound interest than given. 2 years: Only this duration leads to a compound interest of exactly 4347 rupees.

Common Pitfalls:
Some learners incorrectly use simple interest formulas without realizing that the problem clearly mentions compound interest. Others may forget to add the interest to the principal to get the amount A before using the compound interest formula. Another common mistake is failing to check integer values of n logically and instead overcomplicating the equation. For standard exam questions, the correct n is usually a small whole number.

Final Answer:
The money was invested for 2 complete years at 7% per annum compound interest to generate Rs. 4,347 as compound interest on Rs. 30,000.