On a principal sum of Rs. 9500, the simple interest earned over a period of 10 years is equal to 130% of the principal amount. What is the annual rate of simple interest (in percent per annum)?

Introduction / Context:
Questions based on simple interest often ask you to connect principal, rate, time, and the total interest earned. In this problem, you are told that the simple interest earned over 10 years on a principal of Rs. 9500 is 130% of the principal. Instead of directly giving the interest amount, the question gives a percentage of principal, which tests your ability to convert percentages into actual values and then back into the rate of interest per annum using the standard simple interest formula.

Given Data / Assumptions:

• Principal P = Rs. 9500.
• Time T = 10 years.
• Simple interest earned over 10 years is 130% of the principal.
• Interest is calculated using simple interest, not compound interest.
• We assume there are no additional fees or changes in rate during the period.

Concept / Approach:
For simple interest, the standard formula is SI = P * R * T / 100, where SI is simple interest, P is principal, R is annual rate in percent, and T is time in years. Here, we first compute the actual simple interest amount using the information that it is 130% of the principal. Once we know SI, we substitute SI, P, and T in the formula and solve for R. This method directly links the given percentage relationship to the yearly rate of interest.

Step-by-Step Solution:
Step 1: Principal P = 9500 rupees. Step 2: Simple interest is 130% of principal, so SI = 130 * 9500 / 100 = 1.3 * 9500 = 12350 rupees. Step 3: Use the simple interest formula SI = P * R * T / 100. Step 4: Substitute SI = 12350, P = 9500, T = 10 years. Step 5: 12350 = 9500 * R * 10 / 100. Step 6: Simplify the right side: 9500 * 10 / 100 = 950. Step 7: Therefore 12350 = 950 * R. Step 8: Solve for R: R = 12350 / 950 = 13. Step 9: Hence the annual simple interest rate is 13% per annum.

Verification / Alternative check:
To verify, assume rate R = 13% and compute the interest again: SI = 9500 * 13 * 10 / 100 = 9500 * 130 / 100 = 9500 * 1.3 = 12350 rupees. Now compare SI with the principal: 12350 / 9500 = 1.3, which is 130% of the principal, exactly matching the condition in the question. This confirms that the calculated rate of 13% per annum is correct.

Why Other Options Are Wrong:
If R = 12%, the interest would be 9500 * 12 * 10 / 100 = 11400, which is only 120% of the principal. If R = 15%, SI would be 14250, equal to 150% of the principal. If R = 19%, SI would be 18050, which is 190% of the principal. None of these options satisfy the required condition of 130% of the principal, so they are incorrect.

Common Pitfalls:
A typical mistake is to treat 130% of principal as the amount instead of the interest, leading to wrong values. Another error is forgetting to divide by 100 when converting percentage to decimal. Some students also try to average rates or manipulate the numbers without using the formula SI = P * R * T / 100, which usually leads to confusion. Always carefully interpret whether a percentage refers to interest or amount, and then apply the formula systematically.

Final Answer:
Therefore, the annual rate of simple interest is 13% per annum.