Simple Interest — A sum becomes 8 times in 15 years at simple interest. What is the annual rate of interest?

Introduction / Context:
When an amount becomes a multiple of the principal under simple interest, we relate the multiple to the total simple interest accumulated over time.

Given Data / Assumptions:

• A = 8P.
• t = 15 years.
• Simple interest applies.

Concept / Approach:
For simple interest: A = P + SI. If A = 8P, then SI = 7P over 15 years. Since SI = P * r * t, solve for r.

Step-by-Step Solution:
P * r * 15 = 7P.Cancel P: r * 15 = 7.r = 7 / 15 = 0.466666... = 46 2/3% per annum.

Verification / Alternative check:
Annual SI = 46 2/3% of P; in 15 years: (46 2/3%)*15 = 700% of P; A = P + 7P = 8P.

Why Other Options Are Wrong:
45%, 44%, 42 2/3%, 40% do not yield A = 8P in 15 years under simple interest.

Common Pitfalls:
Confusing 46 2/3% with 46.2% or 46.7% rounded.

Final Answer:
46 2/3%