In how many years will a principal of Rs 25000 earn Rs 8275 as compound interest at 10% per annum, when interest is compounded annually?

Introduction / Context:
This question asks you to determine the time period required for a given principal to generate a specified amount of compound interest at a fixed annual rate. It emphasizes understanding the relationship between compound amount, principal, rate, and time, and how to manipulate the standard formula to find time when the interest part, rather than the final amount, is given. This is a typical exam question that checks conceptual clarity and comfort with percentages and powers.

Given Data / Assumptions:

• Principal P = Rs 25000
• Compound interest over n years CI = Rs 8275
• Annual rate of interest r = 10% per annum
• Interest is compounded annually
• We need to find the number of years n

Concept / Approach:
For annual compounding, the amount A after n years is given by A = P * (1 + r)^n. The compound interest CI is defined as CI = A - P. Therefore, CI = P * [(1 + r)^n - 1]. When P, CI, and r are given, we can first compute the amount A as P + CI, then form the ratio A / P and find n such that (1 + r)^n equals that ratio. In many exam problems, the ratio is chosen so that it matches a simple power, making it easy to identify n without complex calculations.

Step-by-Step Solution:
P = 25000, CI = 8275, r = 10% = 0.10 First find the amount A: A = P + CI = 25000 + 8275 = 33275 Now use the compound amount formula: A = P * (1 + r)^n 33275 = 25000 * (1.10)^n Divide both sides by 25000: 33275 / 25000 = (1.10)^n 33275 / 25000 = 1.331 We know 1.10^3 = 1.331, so n = 3 years

Verification / Alternative check:
We can verify by explicitly computing the amount after 3 years at 10%. After 1 year: 25000 * 1.10 = 27500. After 2 years: 27500 * 1.10 = 30250. After 3 years: 30250 * 1.10 = 33275. The compound interest is then 33275 - 25000 = 8275, which matches the given CI. Hence 3 years is correct.

Why Other Options Are Wrong:
If n = 2 years, the amount is only 30250, giving CI = 5250, which is too low. For 4 years, the amount would be 33275 * 1.10 = 36602.50, giving a much larger CI than 8275. Five years would increase the amount even more. Therefore only 3 years matches the required interest exactly.

Common Pitfalls:
A common mistake is to treat the given interest as simple interest and apply the simple interest formula P * r * t / 100, which does not work here. Another pitfall is to forget to add the interest to the principal to form the amount A before applying the compound interest formula. Recognizing the ratio 1.331 as 1.10^3 is a useful shortcut that simplifies the calculation.

Final Answer:
The sum of Rs 25000 will earn Rs 8275 as compound interest in 3 years at 10 percent per annum compounded annually.