Doubling time under simple interest: If a sum of money becomes double at simple interest in 12 years, what is the annual rate of interest?

Introduction / Context:
In simple interest, doubling means the interest earned equals the entire principal. The time to double directly fixes the annual percentage rate using a proportion.

Given Data / Assumptions:

• Amount after 12 years is twice the principal
• Hence interest over 12 years equals 100% of principal

Concept / Approach:
Let rate be r% per annum. For SI, interest over t years is r * t percent of principal. If interest equals 100% in 12 years, then r * 12 = 100 → r = 100 / 12.

Step-by-Step Solution:
r * 12 = 100r = 100 / 12 = 8.333...% per annum = 8⅓%

Verification / Alternative check:
At 8⅓% per annum, 12 years of SI gives 12 * 8⅓% = 100% of principal, so amount = principal + principal = 2P (double).

Why Other Options Are Wrong:
10%, 12%, 14%, and 7½% give interest totals not equal to 100% over 12 years.

Common Pitfalls:
Using compound interest logic or rounding 8⅓% too aggressively can misstate the exact doubling condition for SI.

Final Answer:
8⅓%