Simple Interest – Scaling rate for a larger multiple in the same time: A certain principal becomes 6 times the original at a simple interest rate of 5% per annum. In the same time period, at what simple interest rate (per annum) would the principal become 12 times?

Introduction / Context:
For simple interest, the amount A after t years at annual rate r is A = P * (1 + r * t). When time is fixed, target multiples relate linearly to r through the term (1 + r * t).

Given Data / Assumptions:

• At 5% per year, amount becomes 6P → 1 + 0.05 * t = 6
• Same t required for amount to become 12P → 1 + r * t = 12

Concept / Approach:
First determine t from the first condition, then substitute it into the second equation to solve for the unknown rate r.

Step-by-Step Solution:
1 + 0.05t = 6 → 0.05t = 5 → t = 100 yearsFor 12P: 1 + r * 100 = 12 → r = 11/100 = 0.11 = 11%

Verification / Alternative check:
Using t = 100, at 5%: 1 + 0.05 * 100 = 6 (works). For r = 11%: 1 + 0.11 * 100 = 12 (works).

Why Other Options Are Wrong:
10%, 9%, and 12% yield 11, 10, and 13 as the multiplier respectively, not 12.

Common Pitfalls:
Assuming rate must simply double (from 6x to 12x) without accounting for the initial '+1' in 1 + r * t.

Final Answer:
11%