At what time period (in years) will a principal of Rs. 25,000 yield Rs. 8,275 as compound interest at 10% per annum compounded annually?

Introduction / Context:
This question focuses on determining the time period required for a given principal to earn a specified amount of compound interest. It tests your understanding of the compound interest formula and your ability to relate principal, amount, rate, and time in a financial context.

Given Data / Assumptions:

• Principal P = Rs. 25,000
• Compound interest earned CI = Rs. 8,275
• Rate of interest r = 10% per annum
• Compounding is done annually
• We need to find time T in years

Concept / Approach:
First, compute the final amount A using:
A = P + CIThen use the compound interest amount formula:
A = P * (1 + r / 100)^TWe know P, r, and A, so we must find T. Because the numbers are neat, T will be an integer, so we can check successive powers of (1.1).

Step-by-Step Solution:
Step 1: Compute the amount.A = P + CI = 25000 + 8275 = Rs. 33,275Step 2: Use the formula A = P * (1 + 10 / 100)^T.33275 = 25000 * (1.1)^TStep 3: Divide both sides by 25000.33275 / 25000 = (1.1)^T33275 / 25000 = 1.331Step 4: Check powers of 1.1.(1.1)^2 = 1.21 (too small)(1.1)^3 = 1.331 (exact match)Therefore, T = 3 years.

Verification / Alternative check:
We can verify by directly computing compound interest for 3 years. Amount after 3 years:
A = 25000 * (1.1)^3 = 25000 * 1.331 = 33,275The compound interest is:
CI = 33,275 - 25,000 = 8,275which matches the given CI, so our answer is consistent.

Why Other Options Are Wrong:
2 years: (1.1)^2 = 1.21 gives amount 25,000 * 1.21 = 30,250, interest 5,250, not 8,275.4 years: (1.1)^4 = 1.4641 gives too large an amount.5 or 6 years: These produce even higher amounts and much larger interest, so they do not match the given CI.

Common Pitfalls:
Students sometimes confuse simple interest with compound interest and try to use linear calculations (P * r * T / 100). Another mistake is not adding the interest to the principal to find the amount before using the compound interest formula. Systematically checking powers of (1 + r / 100) helps avoid algebraic errors when the answer is a small integer number of years.

Final Answer:
The required time for Rs. 25,000 to earn Rs. 8,275 as compound interest at 10% per annum is 3 years.