Simple Interest – Scaling the rate with fixed time: A certain principal becomes 3 times at 4% simple interest per annum. In the same time, at what annual simple interest rate would it become 6 times?

Introduction / Context:
When the time is fixed, simple interest amounts scale linearly with the annual rate. We can use the relation A = P * (1 + r * t).

Given Data / Assumptions:

• At 4% per annum, amount becomes 3P → 1 + 0.04t = 3
• Same t, find r so that amount becomes 6P → 1 + r*t = 6

Concept / Approach:
From the first condition, obtain t. Substitute t into the second to find r.

Step-by-Step Solution:
1 + 0.04t = 3 → 0.04t = 2 → t = 50 years1 + r*50 = 6 → r = 5/50 = 0.10 = 10%

Verification / Alternative check:
Proportionality: To go from 3P to 6P, the linear term doubles → rate should double from 4% to 8%? Not exactly; it must satisfy 1 + r*t = 6. Solving gives 10% (not 8%).

Why Other Options Are Wrong:
12%, 8%, 9% do not satisfy 1 + r*50 = 6.

Common Pitfalls:
Assuming rate simply doubles from 4% to 8% without using the +1 term in the simple interest expression.

Final Answer:
10%