If a sum of Rs. 12,500 is invested for 1 year at 12% per annum interest compounded semi-annually (that is, twice a year), then what is the total interest earned in that year?

Introduction:
This question examines the effect of semi annual compounding compared to simple annual interest. The goal is to find the interest earned over 1 year when the nominal annual rate is 12% but compounding occurs twice a year on a principal of Rs. 12,500.

Given Data / Assumptions:
Principal P = Rs. 12,500. Annual nominal rate r = 12% per annum. Compounding frequency = semi annual (two times per year). Time t = 1 year.

Concept / Approach:
For semi annual compounding: Rate per half year = r / 2 = 6%. Number of half years = 2. The amount is: A = P * (1 + 0.06)^2. The compound interest CI is A − P. This will be slightly more than simple interest at 12% for 1 year due to compounding.

Step-by-Step Solution:
Step 1: Compute half yearly rate and periods. Rate per half year = 6%. Number of periods = 2. Step 2: Compute the amount. A = 12500 * (1.06)^2. (1.06)^2 = 1.1236. A = 12500 * 1.1236 = 12500 + 12500 * 0.1236. 12500 * 0.1236 = 1545. So A = 12500 + 1545 = Rs. 14,045. Step 3: Interest earned. CI = A − P = 14,045 − 12,500 = Rs. 1,545.

Verification / Alternative check:
For simple interest at 12% for 1 year, SI would be 12,500 * 12 / 100 = Rs. 1,500. Since semi annual compounding should yield a bit more than simple interest, an answer slightly above 1,500 such as 1,545 is reasonable and matches the precise calculation.

Why Other Options Are Wrong:
Rs. 1,505 and Rs. 1,535 are close but do not match the exact product 12500 * 0.1236. Rs. 1,550 is slightly larger and misaligns with the squared multiplier 1.1236. Rs. 1,450 is less than simple interest and therefore impossible for compound interest at the same nominal rate.

Common Pitfalls:
A common error is to use 12% once for 1 year without adjusting for semi annual compounding. Others may miscalculate (1.06)^2 or forget to subtract the principal to obtain the interest portion only. Always separate the steps of finding the amount and then the interest.

Final Answer:
The total interest earned in 1 year is Rs. 1,545.