If the compound interest received on a certain amount during the 3rd year is Rs 12,100, what will be the compound interest (in rupees) for the 4th year on the same amount at the same rate, if the annual rate of interest is 9%?

Introduction / Context:
In this question, you are given the compound interest earned in the 3rd year and asked to compute the compound interest earned in the 4th year at the same rate. The key idea is that in compound interest, each year's interest is increased by the same percentage rate, because interest is calculated on a growing principal.

Given Data / Assumptions:

• Compound interest during the 3rd year = Rs 12,100.
• Annual rate of interest r = 9%.
• Interest is compounded annually.
• Same principal and same rate apply into the 4th year.

Concept / Approach:
The compound interest earned in successive years follows a geometric progression. Specifically, interest in the (n + 1)th year equals interest in the nth year multiplied by (1 + r/100). Therefore, once we know the interest in the 3rd year and the rate, we can directly get the 4th year interest by multiplying the 3rd year interest by 1.09.

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 12,100 and rate r = 9%. Step 3: Relation between consecutive years: I4 = I3 * (1 + r/100). Step 4: Compute 1 + r/100 = 1 + 9/100 = 1.09. Step 5: Calculate I4 = 12,100 * 1.09 = 12,100 + 1089 = Rs 13,189.
Verification / Alternative check:
You can think of the effective base for the 4th year interest as the amount at the end of the 3rd year, which itself is 9% higher than the amount at the end of the 2nd year. Hence, the 4th year interest is 9% higher than the 3rd year interest, confirming the multiplication by 1.09.
Why Other Options Are Wrong:
Rs 17,080 and Rs 15,669 are much too high and would require a rate higher than 9% or a different base interest in the 3rd year. Rs 14,376 also does not equal 12,100 * 1.09 and therefore does not represent the correct 4th year interest.
Common Pitfalls:
Some candidates mistakenly add 9% of the original principal instead of 9% of the 3rd year's base amount, confusing simple and compound interest. Others may attempt to recompute the entire principal unnecessarily, when a simple ratio approach between consecutive years is enough.
Final Answer:
The compound interest earned in the 4th year will be Rs 13,189.