Simple Interest — How long will a sum invested at 5% per annum simple interest take to increase by 50% of its value?

Introduction / Context:
An increase by 50% means SI = 0.5P. With rate and time known or unknown, use SI = P * r * t to solve for the missing variable.

Given Data / Assumptions:

• r = 5% per annum = 0.05.
• Target increase = 50% of P, i.e., SI = 0.5P.

Concept / Approach:
Use SI = P * r * t ⇒ 0.5P = P * 0.05 * t.

Step-by-Step Solution:
0.5P = 0.05P * t ⇒ 0.5 = 0.05 * t.t = 0.5 / 0.05 = 10 years.

Verification / Alternative check:
At 5% for 10 years: total interest = 50% of P, so amount = 1.5P.

Why Other Options Are Wrong:
7, 12, 15 years do not satisfy 0.05 * t = 0.5.

Common Pitfalls:
Interpreting “increase by 50%” as “becomes 50% of the amount.” It means amount becomes 1.5P.

Final Answer:
10 yr