In how many years will a principal of Rs 1000 amount to Rs 1331 at 10% per annum, when the interest is compounded annually throughout the period?

Introduction / Context:
This question tests the core concept of compound interest and how time, rate of interest, and principal interact to produce a given amount. Instead of directly giving the time period, the question provides the initial principal, the final amount, and the annual compound rate, and asks you to work backward to determine the number of years required. Such questions are common in bank exams and aptitude tests because they check conceptual clarity about the compound interest formula and the ability to manipulate powers and ratios.

Given Data / Assumptions:

• Principal P = Rs 1000
• Amount after n years A = Rs 1331
• Annual rate of interest r = 10% per annum
• Interest is compounded once every year

Concept / Approach:
For compound interest with annual compounding, the relationship between amount and principal is given by the standard formula A = P * (1 + r)^n, where r is written in decimal form and n is the number of years. Here, we know P, A, and r, so we rearrange the formula to solve for the time period n. A useful trick is to first compute the ratio A / P and then recognize it as a power of (1 + r). When the numbers are neat, this ratio often corresponds to a small integer power, which allows a quick mental check without heavy calculation.

Step-by-Step Solution:
Given P = 1000, A = 1331, r = 10% = 0.10 Formula: A = P * (1 + r)^n So, 1331 = 1000 * (1 + 0.10)^n 1331 = 1000 * (1.10)^n Divide both sides by 1000: 1331 / 1000 = (1.10)^n 1331 / 1000 = 1.331 Note that 1.10^2 = 1.21 and 1.10^3 = 1.331 Therefore, (1.10)^3 = 1.331, so n = 3 years

Verification / Alternative check:
We can verify the answer by directly computing the amount year by year. After 1 year, the amount is 1000 * 1.10 = 1100. After 2 years, it becomes 1100 * 1.10 = 1210. After 3 years, it becomes 1210 * 1.10 = 1331. This matches the required amount exactly. Since after 2 years the amount is still less than 1331 and after 3 years it is exactly 1331, 3 years is the only valid solution. No fractional time is needed because the growth is exact at n = 3.

Why Other Options Are Wrong:
2 years would give an amount of 1210, which is less than 1331, so it is too short a period. 4 years would give 1331 * 1.10 = 1464.1, which is greater than the required amount. 5 years would increase the amount even more and therefore does not satisfy the given data. Hence all options other than 3 years are inconsistent with the formula and the given amount.

Common Pitfalls:
A common mistake is to apply the simple interest idea and assume that Rs 1000 grows by Rs 100 every year and therefore takes 3.31 years, which is incorrect for compound interest. Another error is to approximate the ratio 1331 / 1000 without recognizing it as a neat power of 1.10. Some students also forget to convert the percentage 10% to decimal form 0.10 in the formula, which changes the calculation and leads to a wrong time period.

Final Answer:
The required time is 3 years for Rs 1000 to grow to Rs 1331 at 10 percent per annum compounded annually.