Simple Interest – Same time, different multipliers: In a certain time, a principal becomes 4 times at 5% per annum simple interest. In the same duration, at what simple interest rate will the principal become 8 times?

Introduction / Context:
Under simple interest, amount = P * (1 + r * t). Holding time constant, different target multiples give linear equations in r.

Given Data / Assumptions:

• At 5% per year, 1 + 0.05t = 4 → t = 60 years
• Same t, find r where 1 + r*60 = 8

Concept / Approach:
Compute t from the first condition; use it in the second to solve for r.

Step-by-Step Solution:
1 + 0.05t = 4 → 0.05t = 3 → t = 601 + r*60 = 8 → r = 7/60 = 0.116666… = 11 2/3 %

Verification / Alternative check:
Plug back: 1 + 0.116666… * 60 = 1 + 7 = 8 (correct).

Why Other Options Are Wrong:
11 3/5 %, 12 2/3 %, 12 3/5 % correspond to 0.116, 0.126…, 0.126… which do not yield 8P.

Common Pitfalls:
Confusing 4x with 400% interest (it is 300% interest over principal) and mishandling the +1 term.

Final Answer:
11 2/3 %