For a certain principal invested at compound interest, the compound interest for the 3rd year is Rs 125 and for the 4th year is Rs 135. What is the annual rate of interest (in %)?

Introduction / Context:
Rather than giving the total interest or the total amount, this question provides the compound interest earned in the 3rd year and in the 4th year. It checks whether you understand how yearly compound interest grows geometrically and how successive years' interests are related through the rate of interest.

Given Data / Assumptions:

• Compound interest in the 3rd year = Rs 125.
• Compound interest in the 4th year = Rs 135.
• Rate of interest r% per annum, compounded annually.
• Principal is some unknown sum P.
• No deposits or withdrawals occur during the period.

Concept / Approach:
In compound interest, the interest earned in each successive year increases by the same percentage rate. That means the interest in the 4th year equals the interest in the 3rd year multiplied by (1 + r/100). Therefore, by taking the ratio of 4th-year interest to 3rd-year interest, we can directly obtain 1 + r/100 and hence easily find r.

Step-by-Step Solution:
Step 1: Let I3 be the interest in the 3rd year and I4 be the interest in the 4th year. Step 2: Given I3 = Rs 125 and I4 = Rs 135. Step 3: In compound interest, I4 = I3 * (1 + r/100). Step 4: Therefore, 1 + r/100 = I4 / I3 = 135 / 125. Step 5: Compute the ratio: 135 / 125 = 1.08. Step 6: So 1 + r/100 = 1.08, giving r/100 = 0.08 and r = 8.
Verification / Alternative check:
If the rate is 8%, each year's interest is multiplied by 1.08. Starting from 125 in the 3rd year, the 4th-year interest should be 125 * 1.08 = 135, which matches the given data. This confirms that r = 8% is consistent.
Why Other Options Are Wrong:
A rate of 9% would give 125 * 1.09 = 136.25, not 135. 10% would give 125 * 1.10 = 137.5, again not matching the given 135. 12% would produce 125 * 1.12 = 140, clearly not correct.
Common Pitfalls:
A common mistake is to treat 125 and 135 as interest for the first two years or to try to compute the principal directly, which is unnecessary. Others may incorrectly average the two interest values instead of using their ratio.
Final Answer:
The annual rate of compound interest is 8%.