Simple Interest – Time to double at 12% per annum: In how many years will a sum of money become twice its principal at 12% per annum under simple interest?

Introduction / Context:
Under simple interest, doubling time is computed from the fact that the interest must equal the principal. This yields a direct formula for the time required given the annual rate.

Given Data / Assumptions:

• Target amount A = 2P
• Rate r = 12% per annum
• Simple interest relation I = P * r * t / 100

Concept / Approach:
For doubling, I = P. So P = P * r * t / 100 ⇒ t = 100 / r years. Substitute r = 12 to get the exact time in years and months.

Step-by-Step Solution:
t = 100 / 12 years = 25 / 3 years25 / 3 years = 8 + 1/3 years = 8 years 4 months

Verification / Alternative check:
At 12% per annum, annual interest is 12% of P. Over 8 1/3 years, interest totals (12% * 8 1/3) = 100% of P, so A = 2P, confirming the result.

Why Other Options Are Wrong:
6 years 9 months, 7 years 6 months, and 8 years 6 months correspond to different rates or targets; only 8 years 4 months precisely equals 100/12 years.

Common Pitfalls:
Using compound interest rules (e.g., 72-rule) leads to approximations that are not required here. Simple interest gives an exact linear relation.

Final Answer:
8 years 4 months