An amount becomes double of itself in 15 years at simple interest. What is the annual rate of simple interest (in % per annum)?

Introduction / Context:
This question tests the core simple interest doubling concept. Under simple interest, the amount after t years is A = P + SI, and SI = P * r * t / 100. If an amount doubles, it means A = 2P, so SI must equal P. This immediately creates a direct equation for r. Unlike compound interest, doubling time under simple interest is linear and depends directly on time (no exponential growth).

Given Data / Assumptions:

• Simple interest is used
• Time, t = 15 years
• Amount doubles: A = 2P
• SI formula: SI = P * r * t / 100
• Amount under SI: A = P + SI

Concept / Approach:
If A = 2P, then:
P + SI = 2P SI = P Substitute into SI formula and solve for r.

Step-by-Step Solution:
SI = P * r * t / 100 Given doubling in 15 years => SI = P So, P * r * 15 / 100 = P Cancel P on both sides: r * 15 / 100 = 1 r = 100 / 15 r = 6.666... Rate ≈ 6.66% per annum

Verification / Alternative check:
At 6.666...% per annum, SI for 15 years is P*6.666...*15/100 = P*1 = P. So A = P + P = 2P, confirming the amount doubles exactly under SI.

Why Other Options Are Wrong:
7.85% and 9.41% would make SI greater than P in 15 years, producing more than double. 4.21% and 5% would produce less than P as SI, so the amount would be less than double.

Common Pitfalls:
Applying compound doubling logic (like rule of 72) even though this is simple interest, or forgetting that under SI, doubling implies SI equals principal exactly for the given period.

Final Answer:
The required simple interest rate is approximately 6.66% per annum.