The simple interest accrued on an amount of Rs 28,500 over a period of 7 years is Rs 23,940. What is the annual rate of simple interest per cent per annum?

Introduction / Context:
This question focuses on finding the annual rate of simple interest when the principal, total interest, and duration are given. Such problems are classic in the topic of simple interest and feature regularly in aptitude tests, banking exams, and finance related questions.

Given Data / Assumptions:

• Principal, P = Rs 28,500.
• Total simple interest, SI = Rs 23,940.
• Time period, T = 7 years.
• Rate of interest per annum, R%, is unknown and needs to be determined.

Concept / Approach:
The basic formula for simple interest is:
SI = (P * R * T) / 100From this relation, when SI, P, and T are known, we can solve for R using:
R = (SI * 100) / (P * T)Substituting the given values and simplifying will lead to the required rate of interest.

Step-by-Step Solution:
Step 1: Substitute the known values into the formula for R.R = (SI * 100) / (P * T)R = (23940 * 100) / (28500 * 7)Step 2: Compute the denominator.Denominator = 28500 * 7 = 199,500Step 3: Compute the numerator.Numerator = 2,394,000Step 4: Divide numerator by denominator.R = 2,394,000 / 199,500R = 12Therefore, the annual simple interest rate is 12%.

Verification / Alternative check:
We can verify this by computing the interest using 12% and comparing it with Rs 23,940. With R = 12%:
SI = (28500 * 12 * 7) / 100= (28500 * 84) / 100= 2,394,000 / 100 = 23,940This exactly matches the given interest, confirming that 12% is correct.

Why Other Options Are Wrong:

• 10.5%, 11%, and 12.5% each produce an interest amount different from Rs 23,940 when substituted into the simple interest formula.
• Only 12% yields the exact stated interest over 7 years on Rs 28,500.

Common Pitfalls:
Some candidates may incorrectly multiply or divide during the calculation of R, especially when handling larger products like 28,500 * 7. Others may try to reduce fractions too early and get lost in intermediate steps. A systematic approach, writing out each step, and simplifying carefully reduces the chance of such errors.

Final Answer:
The annual simple interest rate is 12% per annum.