Simple Interest — A sum of money doubles itself in 20 years under simple interest. What is the annual rate of simple interest (per cent per year)?

Introduction / Context:
Many aptitude questions ask for the rate of simple interest when the final amount is a given multiple of the original principal. Under simple interest, growth is linear with time, so doubling or tripling leads to direct proportional relations between time, rate, and principal.

Given Data / Assumptions:

• The amount becomes double of the principal in 20 years.
• Interest is simple, applied per annum.
• Let principal be P (any positive amount).

Concept / Approach:
For simple interest: Amount A = P + SI, and SI = P * r * t, where r is rate per year (in decimal) and t is time in years.

Step-by-Step Solution:
Given A = 2P in 20 years.So SI = A - P = 2P - P = P.But SI = P * r * t.Hence P = P * r * 20.Cancel P (P > 0): 1 = r * 20.Therefore r = 1 / 20 = 0.05 = 5% per annum.

Verification / Alternative check:
If r = 5%, then SI in 20 years = P * 0.05 * 20 = P, so A = P + P = 2P, which matches the condition.

Why Other Options Are Wrong:
4% or 8% or 10% would produce amounts not exactly equal to 2P in 20 years under simple interest.

Common Pitfalls:
Confusing simple interest with compound interest; for simple interest, use linear SI = P * r * t.

Final Answer:
5%