Simple Interest – Time to quadruple when doubling time is known: If a certain sum doubles itself in 8 years at simple interest, in how many years will it become four times the principal?

Introduction / Context:
In simple interest, growth is linear with time. If we know the time to double, we can scale proportionally to find the time to quadruple the principal.

Given Data / Assumptions:

• Doubling time t2 = 8 years
• Simple interest model

Concept / Approach:
Doubling at SI means interest equals P over 8 years, so r = 1 / 8 = 12.5% per annum. For quadrupling (A = 4P), interest must be 3P, so time t4 = 3P / (P * r) = 3 / r.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 16/12/20 years: inconsistent with r = 12.5%.
• 32 years: overestimates required time.

Common Pitfalls:

• Treating the process as compounding.
• Confusing quadruple of P with four times the interest.

Final Answer:
24 years.