Simple Interest — At what annual rate will the simple interest in 10 years be one-fifth of the amount?

Introduction / Context:
The phrase “simple interest is one-fifth of the amount” relates SI to A (not to P). Convert that relation to P and SI to find the rate over the given time.

Given Data / Assumptions:

• In 10 years, SI = (1/5) * A.
• A = P + SI (simple interest).

Concept / Approach:
Let SI = A / 5. Since A = P + SI, substitute to relate SI to P alone and then use SI = P * r * t.

Step-by-Step Solution:
Given SI = A / 5 and A = P + SI.So SI = (P + SI) / 5 ⇒ 5SI = P + SI ⇒ 4SI = P.Hence SI = P / 4 over 10 years.But SI = P * r * t ⇒ P / 4 = P * r * 10.Cancel P: 1 / 4 = 10r ⇒ r = 1 / 40 = 0.025 = 2.5% per annum.

Verification / Alternative check:
At 2.5% for 10 years, SI = 25% of P; A = 125% of P; SI / A = 0.25 / 1.25 = 1/5, which matches.

Why Other Options Are Wrong:
2%, 1%, 4%, 5% do not satisfy SI = A / 5 at 10 years.

Common Pitfalls:
Misreading “one-fifth of the amount” as “one-fifth of the principal.” They are different statements.

Final Answer:
2.5%