What is the simple interest on Rs 7,500 at a rate of 10% per annum for a period of 5 years, assuming standard simple interest calculations?

Introduction / Context:
This is a direct and basic application of the simple interest formula. The principal, rate, and time are all given, and the question asks only for the interest earned over the specified period. Such problems are often used early in the study of interest calculations to build familiarity with the formula and the meaning of percentage rates per annum.

Given Data / Assumptions:
- Principal P = Rs 7,500. - Annual simple interest rate R = 10 percent per annum. - Time T = 5 years. - Interest is calculated using simple interest. - Required quantity is the simple interest SI over 5 years.

Concept / Approach:
The formula for simple interest is SI = (P * R * T) / 100. We substitute the values of principal, rate, and time directly into this formula. There is no need to find the total amount unless explicitly asked, but we can always compute it as A = P + SI as an additional step. Here we focus on the interest only, which is straightforward.

Step-by-Step Solution:
Step 1: Identify P = Rs 7,500, R = 10 percent, T = 5 years. Step 2: Use SI = (P * R * T) / 100. Step 3: Substitute: SI = (7,500 * 10 * 5) / 100. Step 4: Compute 7,500 * 10 = 75,000. Step 5: Multiply 75,000 * 5 = 3,75,000. Step 6: Divide by 100: SI = 3,75,000 / 100 = Rs 3,750. Step 7: Hence, the simple interest for 5 years is Rs 3,750.

Verification / Alternative check:
We can also think in terms of yearly interest. At 10 percent per annum on Rs 7,500, yearly interest is (7,500 * 10 * 1) / 100 = Rs 750. Over 5 years, total interest is 750 * 5 = Rs 3,750. This matches the result obtained from the formula, confirming the calculation.

Why Other Options Are Wrong:
Rs 2,750 would correspond to a lower effective rate or shorter time. Rs 1,750 and Rs 750 are even smaller and do not represent 10 percent per year for 5 full years. Only Rs 3,750 equals 10 percent of the principal each year, multiplied by 5 years.

Common Pitfalls:
Students may forget to divide by 100 after multiplying P, R, and T, which would give 3,75,000 instead of 3,750. Another error is to multiply the principal by the rate only once and forget to include time. Writing the full formula explicitly and following it step by step avoids such mistakes.

Final Answer:
The simple interest for 5 years is Rs 3,750.