If Rs 2 produces Rs 11 as simple interest over a period of 30 years, what is the annual rate of simple interest in percent per annum for this very long term investment?

Introduction / Context:
This question presents a very small principal and interest but over a very long period of 30 years. It asks for the annual simple interest rate that would produce a total interest of Rs 11 on a principal of Rs 2. The main skill tested is correct substitution into and rearrangement of the simple interest formula to solve for the annual rate.

Given Data / Assumptions:
- Principal P = Rs 2. - Simple interest earned SI = Rs 11. - Time period T = 30 years. - Interest is calculated using simple interest. - Required quantity is the annual rate R in percent per annum.

Concept / Approach:
The simple interest formula SI = (P * R * T) / 100 can be rearranged to find the rate as R = (SI * 100) / (P * T). We substitute the known values for SI, P, and T and then simplify. Because the principal is small and the time is large, the rate obtained is relatively high. However, mathematically, the process is the same as for any other simple interest problem.

Step-by-Step Solution:
Step 1: Start with SI = (P * R * T) / 100. Step 2: Rearrange for R: R = (SI * 100) / (P * T). Step 3: Substitute SI = 11, P = 2, T = 30. Step 4: Compute denominator P * T = 2 * 30 = 60. Step 5: Compute numerator SI * 100 = 11 * 100 = 1,100. Step 6: Divide numerator by denominator: R = 1,100 / 60. Step 7: Compute 1,100 / 60 = 18.3333 recurring. Step 8: Round to two decimal places to get R ≈ 18.33 percent per annum.

Verification / Alternative check:
Verify by recalculating SI with R = 18.33 percent. SI ≈ (2 * 18.33 * 30) / 100. First 2 * 18.33 = 36.66. Then 36.66 * 30 ≈ 1,099.8. Dividing by 100 gives SI ≈ 10.998, which is very close to 11, with the tiny difference due to rounding of the rate. If we keep more decimal places for R, the interest matches 11 exactly. This confirms that 18.33 percent is the correct approximate rate.

Why Other Options Are Wrong:
At 17.25 percent, the interest would be (2 * 17.25 * 30) / 100 = 10.35, which is less than 11. At 18.14 percent, interest is about 10.884, still smaller than 11. At 17.35 percent, the interest is also below 11. Among the options, 18.33 percent is the only rate that produces an interest essentially equal to Rs 11 over 30 years on Rs 2.

Common Pitfalls:
Learners may mistakenly treat SI as the final amount, or may forget to multiply by 100 when solving for R. Some may be surprised by the large rate and suspect a calculation error. However, with such a tiny principal over a long time, a high rate is necessary to earn Rs 11. Following the formula carefully shows that the result is consistent.

Final Answer:
The annual rate of simple interest is approximately 18.33% per annum.