On a principal of Rs. 30000, the compound interest at 7% per annum is Rs. 4347. For how many years was the money invested, assuming annual compounding?

Introduction / Context:
Instead of finding the amount or interest given the time, this problem reverses the process and asks for the time period, given the principal, rate, and compound interest. This is a useful test of understanding the compound interest relationship between amount and time. The candidate must recognise that the compound interest implies a specific growth factor over the period and then identify the number of years that correspond to that factor.

Given Data / Assumptions:

• Principal P = Rs. 30000.
• Compound interest CI = Rs. 4347.
• Rate r = 7% per annum.
• Interest is compounded annually.
• We need to find the time period n in years.

Concept / Approach:
First we compute the final amount A by adding the compound interest to the principal: A = P + CI. Then we use the compound interest amount formula A = P * (1 + r) ^ n, with r in decimal form. Because the rate and principal are known, we can compute the ratio A / P and see which integer power of (1 + r) equals that ratio. For neat examination values, we usually find that n is a small whole number such as 2 or 3.

Step-by-Step Solution:
Step 1: Compute the amount: A = P + CI = 30000 + 4347 = 34347. Step 2: Convert the rate to decimal form: r = 7% = 0.07. Step 3: The amount formula is A = P * (1 + r) ^ n. Step 4: Compute the ratio A / P = 34347 / 30000. Step 5: Calculate this ratio: 34347 / 30000 = 1.1449. Step 6: Now compute (1.07) ^ 2 = 1.1449. Step 7: We see that (1 + r) ^ 2 equals exactly A / P, so n = 2 years. Step 8: Therefore, the money was invested for 2 years.

Verification / Alternative check:
To verify, we can compute the compound interest for 2 years directly. With P = 30000 and r = 7%, the amount after one year is 30000 * 1.07 = 32100. After the second year, the amount is 32100 * 1.07 = 34347. The compound interest is 34347 - 30000 = 4347, which matches the given interest. This confirms that the time period of 2 years is correct. Checking for 3 years or more would produce much larger amounts and interests, which would not match the given data.

Why Other Options Are Wrong:
If n were 3 years, the growth factor would be (1.07) ^ 3, which is greater than 1.1449, leading to an amount higher than 34347. Four or five years would produce even larger growth factors and amounts, further away from the given condition. One year at 7% would give an amount of only 32100, with interest 2100, far smaller than 4347. Therefore, 2 years is the only period that fits the data exactly.

Common Pitfalls:
A common mistake is to attempt to solve for n algebraically using logarithms, which is correct in general but unnecessary here and can lead to rounding issues. Another error is confusing simple interest and compound interest and trying to use a linear relation like CI = P * r * n directly for compound interest, which fails when interest is compounded. Some learners also forget to convert the rate into decimal form or miscalculate powers of 1.07. Recognising that examination questions often have neat integer time periods helps guide the solution approach.

Final Answer:
The period for which Rs. 30000 was invested at 7% per annum to earn compound interest of Rs. 4347 is 2 years, corresponding to option A.