If the simple interest on ₹1 for a period of 1 month is 1 paisa, what is the corresponding annual rate of interest in percent per annum?

Introduction / Context: This question is about simple interest, one of the most basic topics in arithmetic and banking mathematics. It connects the interest earned over a short period, namely one month, to the annual rate of interest. Understanding how to convert between periods is essential for handling savings, loans and investment problems in exams and in real life. Given Data / Assumptions:

• Principal P = ₹1.
• Time T = 1 month.
• Simple interest for this period is 1 paisa.
• 1 paisa = ₹0.01.
• We assume 1 year = 12 months and use the simple interest formula with T expressed in years.

Concept / Approach: The simple interest formula is:

• Simple interest SI = (P * R * T) / 100, where R is the rate percent per annum and T is time in years.
• We know SI, P and T, and we need to solve for R.
• Convert 1 month into years as T = 1/12.
• Substitute values and rearrange to find R.

Step-by-Step Solution: Step 1: Convert the given interest into rupees: 1 paisa = ₹0.01, so SI = 0.01. Step 2: Principal P = 1 and time T = 1 month = 1/12 year. Step 3: Use the simple interest formula: SI = (P * R * T) / 100. Step 4: Substitute values: 0.01 = (1 * R * (1/12)) / 100. Step 5: Simplify the right side: (R * 1/12) / 100 = R / 1200. Step 6: So 0.01 = R / 1200, which implies R = 0.01 * 1200. Step 7: Compute R: 0.01 * 1200 = 12. Step 8: Therefore the rate of interest is 12% per annum. Verification / Alternative check: Step 1: Assume R = 12% per annum and recompute SI for T = 1/12 year and P = 1. Step 2: SI = (1 * 12 * 1/12) / 100 = (12/12) / 100 = 1/100 = 0.01. Step 3: This matches the given simple interest of ₹0.01 (1 paisa), confirming the calculation is correct. Why Other Options Are Wrong: Option 10% would give SI = (1 * 10 * 1/12) / 100 = 10/1200 ≈ 0.0083, which is less than 0.01. Option 8% gives SI = (1 * 8 * 1/12) / 100 ≈ 0.0067, still smaller than required. Option 6% yields an even smaller interest, around 0.005, not equal to 1 paisa. Option 15% produces SI ≈ 0.0125, which is larger than the given 0.01. Common Pitfalls: One common mistake is to treat 1 month as 1 year, which leads to a huge error in the rate. Another error is mis-converting paisa to rupees, such as taking 1 paisa as 0.1 rupee instead of 0.01 rupee. Some students forget to divide by 100 in the simple interest formula or misplace decimal points while solving for R. Final Answer: The rate of interest per annum is 12%.