Simple Interest – Time to treble when doubling time is known: At a certain simple interest rate, a sum doubles itself in 10 years. In how many years will it become three times the principal?

Introduction / Context:
From the doubling time under SI, we can derive the rate and then compute the time to reach any other multiple of P, such as 3P (treble).

Given Data / Assumptions:

• Doubling time = 10 years
• Simple interest model

Concept / Approach:
Doubling means P * r * 10 = P ⇒ r = 1 / 10 = 10%. For trebling (A = 3P), interest must be 2P, so t = 2P / (P * r) = 2 / 0.10 = 20 years.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 15 / 12 / 25 years: inconsistent with r = 10%.
• 30 years: overestimates time.

Common Pitfalls:

• Treating SI as compound interest.

Final Answer:
20 years.