If the simple interest on a certain sum of money for 2 years at 5% per annum is Rs 50, then what is the compound interest on the same principal at the same rate for the same time?

Introduction:
This question connects simple interest and compound interest for the same principal, rate, and time period. It first gives simple interest and then asks for compound interest, which is a very common pattern in competitive exams to test understanding of both concepts together.

Given Data / Assumptions:

• Simple interest SI = Rs 50
• Time t = 2 years
• Rate r = 5% per annum
• Same principal, rate, and time are used for both SI and CI
• We need compound interest CI for 2 years at 5%

Concept / Approach:
First, find the principal from the simple interest formula:
SI = P * r * t / 100Then use the compound interest amount formula:
A = P * (1 + r/100)^tand compute CI as:
CI = A - P

Step-by-Step Solution:
Step 1: Use simple interest to find principal.SI = P * r * t / 10050 = P * 5 * 2 / 10050 = P * 10 / 10050 = 0.10 * PP = 50 / 0.10 = Rs 500Step 2: Compute amount with compound interest.r = 5% per annum, t = 2 yearsA = 500 * (1 + 5 / 100)^2A = 500 * (1.05)^2(1.05)^2 = 1.1025A = 500 * 1.1025 = Rs 551.25Step 3: Find compound interest.CI = A - P = 551.25 - 500 = Rs 51.25

Verification / Alternative check:
We can also compare SI and CI. For two years, SI is Rs 50, which is Rs 25 per year. With CI, the second year earns interest on principal plus first year interest. That extra interest is about 5% of Rs 25, which is Rs 1.25. So CI should be Rs 50 + Rs 1.25 = Rs 51.25, matching our calculation.

Why Other Options Are Wrong:

• Rs 61.25: Overestimates the compound interest by adding more than the reasonable extra interest.
• Rs 51: Underestimates slightly and does not account fully for compounding.
• Rs 42: Too low; even simple interest is Rs 50.
• Rs 55: Does not match the precise compounding calculation.

Common Pitfalls:
Students may forget to convert the rate to decimal form or miscalculate (1.05)^2. Others might wrongly use the simple interest formula for compound interest. Always remember that compound interest for two years is slightly higher than simple interest due to interest on interest in the second year.

Final Answer:
The compound interest on the sum for 2 years at 5% per annum is Rs 51.25.