In what time will Rs. 1000 amount to Rs. 1331 at 10% per annum compounded annually?

Introduction / Context:
This is a direct application of the compound interest formula to find the time needed for a principal to grow to a given amount at a known annual rate with annual compounding. The numbers are chosen to produce an exact power of a simple factor.

Given Data / Assumptions:

• Principal P = Rs. 1000.
• Amount A = Rs. 1331.
• Rate of interest r = 10% per annum.
• Interest is compounded annually.
• Time in years t is to be determined.

Concept / Approach:

The compound interest formula for annual compounding is A = P * (1 + r / 100)^t. We substitute the known values and solve for the exponent t. Because the numbers are clean, we expect (1 + r / 100)^t to match a simple power such as (1.1)^t.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

After 1 year the amount is only Rs. 1100, not 1331. After 2 years it is Rs. 1210. Even after 4 years the amount would exceed Rs. 1331. Therefore, only 3 years match the required amount exactly, and the other time choices are not correct.

Common Pitfalls:

Some learners mistakenly apply simple interest, solving 1000 + 1000 * 10 * t / 100 = 1331, which gives a non integer value and does not match the compound interest setting. Others may try to interpolate between years rather than checking the powers of 1.10 directly. Remember that compound growth is exponential, so exact powers often appear in exam style problems.

Final Answer:

The required time is 3 years.