When does simple interest equal the principal? If the simple interest for 5 years equals 40% of the principal, after how many years will the simple interest be equal to the principal itself?

Introduction / Context:
Under simple interest, the interest increases linearly with time. If we know what fraction of principal the interest becomes in a known period, we can deduce the annual rate and predict when the interest will equal the entire principal (i.e., 100%).

Given Data / Assumptions:

• SI in 5 years = 40% of principal
• Simple interest rate is constant per year

Concept / Approach:
If SI in 5 years is 0.40P, then yearly interest is 0.40P / 5 = 0.08P → r = 8% per annum. To have SI = 100% of principal, we need r * t = 100% → t = 100 / r years.

Step-by-Step Solution:
From 5 years: r = 40% / 5 = 8% p.a.Set SI = P → r * t = 100%t = 100 / 8 = 12.5 years12.5 years = 12 years 6 months

Verification / Alternative check:
Each year adds 8% of P. After 12 years, SI = 96% of P; after half a year more (4%), total SI = 100% of P.

Why Other Options Are Wrong:
12 years 3 months or 12 years 4 months give less than 100%; 12 years 9 months gives more than 100%.

Common Pitfalls:
Confusing 40% in 5 years with 40% per year or mixing SI with compound interest logic.

Final Answer:
12 years 6 months