A sum of Rs 12,500 amounts to Rs 15,500 in 4 years at the rate of simple interest. What is the rate of interest per annum for this simple interest investment?

Introduction / Context:
This problem is a direct application of the simple interest formula to find the rate of interest when the principal, final amount, and time are given. It reinforces the idea that interest under simple interest grows linearly with time and that the rate can be computed by comparing the interest earned to the principal over the given period.

Given Data / Assumptions:

Principal P = Rs 12,500.
Amount after 4 years, A = Rs 15,500.
Time T = 4 years.
Rate of interest per annum is r%, unknown.
Simple interest SI = A - P.
Formula: SI = (P * r * T) / 100.

Concept / Approach:
First, we find the total simple interest by subtracting the principal from the final amount. Then we use the simple interest formula to relate SI, P, r, and T, and solve for r. Because the values are neat, the resulting rate will be an exact percentage that matches one of the options.

Step-by-Step Solution:
Step 1: Compute simple interest: SI = A - P = 15500 - 12500 = 3000. Step 2: Use SI = (P * r * T) / 100. Step 3: Substitute SI = 3000, P = 12500, T = 4. Step 4: 3000 = (12500 * r * 4) / 100. Step 5: Simplify numerator: 12500 * 4 = 50000. Step 6: So, 3000 = (50000 * r) / 100 = 500r. Step 7: Therefore, r = 3000 / 500 = 6. Step 8: Hence, the rate of interest per annum is 6%.

Verification / Alternative check:
Verify by recomputing the amount using r = 6%. SI = (12500 * 6 * 4) / 100 = (12500 * 24) / 100 = 3000. Then A = P + SI = 12500 + 3000 = 15500, which matches the given amount. This confirms that the rate is correct.

Why Other Options Are Wrong:
If the rate were 3%, 4%, 5%, or 7%, the interest would differ from 3000. For example, at 5% for 4 years, SI would be (12500 * 5 * 4) / 100 = 2500, and at 7% it would be 3500. These do not match the required 3000, so those options are not correct.

Common Pitfalls:
Typical errors include confusing amount with interest, or forgetting to subtract the principal before computing the rate. Some also mix up simple and compound interest formulas. Carefully identify SI = A - P first, then apply the simple interest formula to avoid confusion.

Final Answer:
The rate of simple interest per annum is 6%.