Simple Interest – Rate when amount becomes 8/5 of principal in 5 years: A sum becomes (8/5) times itself in 5 years under simple interest. Find the annual rate percent.

Introduction / Context:If a final amount is expressed as a multiple of principal under simple interest, the interest portion is the excess over 1 times principal. This gives a direct fraction for I / P and leads to the annual rate via the standard formula.

Given Data / Assumptions:

• A = (8/5) P
• Time t = 5 years
• Simple interest I = A − P

Concept / Approach:Compute the fraction I / P = (8/5 − 1) = 3/5. Then use r = (I / (P * t)) * 100 = ((3/5) / 5) * 100.

Step-by-Step Solution:I / P = 3 / 5r = (I / (P * t)) * 100 = ((3/5) / 5) * 100 = (3/25) * 100 = 12%

Verification / Alternative check:At 12% per annum for 5 years, total interest is 60% of P; amount is 160% of P = (8/5) P, confirming the statement.

Why Other Options Are Wrong:5%, 8%, and 10% produce smaller multiples than 8/5 over 5 years; 15% gives too large a multiple under simple interest.

Common Pitfalls:Confusing simple interest with compound interest may lead to solving (1 + r)^t = 8/5, which is not applicable here. Use linear SI relations.

Final Answer:12%