Simple Interest — In how many years will a sum become four times itself at 12% per annum simple interest?

Introduction / Context:Becoming four times under simple interest means the interest earned equals three times the principal over a certain time at a given rate.

Given Data / Assumptions:

• Target: Amount A = 4P.
• Rate r = 12% per annum.
• Simple interest formula applies.

Concept / Approach:For simple interest: SI = P * r * t and A = P + SI. If A = 4P, then SI = 3P. Hence solve P * r * t = 3P.

Step-by-Step Solution:SI = 3P.P * r * t = 3P ⇒ r * t = 3.Given r = 12% = 0.12, so 0.12 * t = 3.t = 3 / 0.12 = 25 years.

Verification / Alternative check:At 12% for 25 years: SI = P * 0.12 * 25 = 3P; Amount = P + 3P = 4P.

Why Other Options Are Wrong:22, 27, or 28 years do not satisfy r * t = 3 with r = 0.12.

Common Pitfalls:Using compound interest logic; here growth is linear.

Final Answer:25 yr