On a principal of ₹9,500, the simple interest earned over 10 years is equal to 130% of the principal amount. What is the annual rate of simple interest (in % per annum)?

Introduction:
This question tests a clean proportional use of the simple interest formula when interest is expressed as a percentage of the principal. Under simple interest, SI grows linearly with time, so if you know SI as a multiple of principal and the time duration, the rate is obtained directly without needing any complicated calculations.

Given Data / Assumptions:

• Principal P = ₹9,500
• Time t = 10 years
• Simple interest earned SI = 130% of P = 1.30P
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Substitute SI = 1.30P into the simple interest formula. Since P appears on both sides, it cancels out. This is the main shortcut: when SI is given as a percentage (or multiple) of principal, you can solve for r using only that percentage and time.

Step-by-Step Solution:
SI = (P * r * t) / 100 Given SI = 1.30P and t = 10 1.30P = (P * r * 10) / 100 Cancel P: 1.30 = (10r) / 100 1.30 = r / 10 r = 13

Verification / Alternative check:
At 13% for 10 years: SI = (9500 * 13 * 10)/100 = 9500 * 1.30 = 12350, which is exactly 130% of 9500. This confirms the rate is correct.

Why Other Options Are Wrong:
12% gives SI = 120% of P in 10 years, too low. 15% gives 150%, too high. 19% is far too high. 10% gives only 100% in 10 years.

Common Pitfalls:
Interpreting 130% as 0.13 instead of 1.30, or forgetting that “130% of principal” refers to interest (not amount).

Final Answer:
The annual simple interest rate is 13% per annum.