The compound interest on Rs 30,000 at 7% per annum amounts to Rs 4,347. For how many years (whole years) was the sum invested?

Introduction / Context:
This question gives us the principal, the annual compound interest rate, and the total compound interest earned, and asks for the time in years. Because both the rate and the time are in whole years with annual compounding, we can use the compound interest formula to compute the amount for different integer values of time and match the one that produces the given interest. This problem reinforces familiarity with typical growth patterns at standard rates like 7%.

Given Data / Assumptions:

• Principal P = Rs 30,000.
• Rate r = 7% per annum.
• Compound interest CI = Rs 4,347.
• Compounding is annual.
• We must find the number of years t (an integer) such that the CI matches the given value.

Concept / Approach:
For annual compounding, the amount after t years is A = P * (1 + r/100)^t. The compound interest is CI = A - P. Thus, P * [(1 + r/100)^t - 1] should equal the given interest, 4,347. We can try small integer values of t, such as 1, 2, 3, and so on, and see which value makes the interest match. This is very efficient in an exam setting where t is expected to be a small whole number.

Step-by-Step Solution:
We have CI = 4,347, P = 30,000 and r = 7%. For t = 1 year: A = 30,000 * 1.07 = 32,100, so CI = 2,100 (too small). For t = 2 years: A = 30,000 * (1.07)^2. Compute (1.07)^2 = 1.1449, so A = 30,000 * 1.1449 = 34,347. So CI for 2 years = 34,347 - 30,000 = 4,347, which matches the given value. Hence, the required time is t = 2 years.

Verification / Alternative check:
To be thorough, we can check t = 3 years as well. For 3 years, A = 30,000 * (1.07)^3, which would be 30,000 * 1.225043 = 36,751.29 (approximately), giving CI ≈ 6,751.29, which is much higher than 4,347. Thus, the only integer time that fits the given interest amount is 2 years. Therefore, our answer is uniquely determined and consistent with the data.

Why Other Options Are Wrong:
For 1 year, the interest is only Rs 2,100, not Rs 4,347. For 3 years, the interest exceeds Rs 6,700. For 4 or 5 years, the interest becomes even larger as compound growth accelerates. Hence, none of these durations will yield exactly Rs 4,347 in compound interest on Rs 30,000 at 7% per annum.

Common Pitfalls:
Learners sometimes miscalculate powers like (1.07)^2 or misinterpret the given Rs 4,347 as the final amount instead of the interest. It is important to keep track of whether the problem is giving CI or A and to subtract or add the principal correctly. Another error is assuming the time must be fractional; exam questions of this type almost always use small integer values of t that can be quickly tested.

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