At what rate of simple interest, expressed as percent per annum, will a sum of money double itself in 8 years?

Introduction / Context:
This question uses the standard simple interest formula to find the rate of interest required for a sum to double in a given period. Time value of money concepts like this are common in banking and finance aptitude problems. Knowing how to quickly determine such a rate is very useful for exam speed and for understanding basic financial planning ideas.

Given Data / Assumptions:

We have a principal sum of money, say P rupees.
The sum doubles in 8 years, so the final amount after 8 years is 2P.
Interest is calculated on a simple interest basis, not compounded.
We need to find the rate of interest per annum r, expressed as a percentage.

Concept / Approach:
Under simple interest, the amount A after time t years at rate r percent per annum on principal P is given by A = P + (P * r * t) / 100. If the sum doubles, then A = 2P. This condition gives us an equation in r and t. Since t is known (8 years), we can solve directly for r. The calculation cancels P, so the actual size of the principal does not matter.

Step-by-Step Solution:
Let principal be P and rate be r percent per annum. Under simple interest, amount A after t years is A = P + (P * r * t) / 100. Here t = 8 years and A = 2P, because the sum doubles. So 2P = P + (P * r * 8) / 100. Subtract P from both sides: 2P - P = (P * r * 8) / 100. This gives P = (P * r * 8) / 100. Cancel P on both sides (P is not zero), giving 1 = (r * 8) / 100. Therefore r * 8 = 100, so r = 100 / 8. Hence r = 12.5 percent per annum.

Verification / Alternative check:
We can test the answer with assumed principal P = 100. At 12.5 percent per annum, simple interest per year is 12.5 rupees. Over 8 years, total interest is 8 * 12.5 = 100 rupees. So the amount becomes 100 + 100 = 200, which is double the principal, confirming that 12.5 percent is correct.

Why Other Options Are Wrong:
Option 13.5 percent would produce total interest of 108 on a principal of 100 over 8 years, resulting in amount 208, which is more than double.
Option 11.5 percent would give total interest of 92 on a principal of 100, resulting in amount 192, which is less than double.
Option 14.5 percent would yield even higher total interest of 116 on principal 100, giving amount 216, again not equal to exactly double.

Common Pitfalls:
Some learners mistakenly apply compound interest formulas, which are not needed here, since the problem clearly refers to simple interest.
Others forget to set the amount equal to 2P when a sum doubles and instead set the interest equal to 2P, which is incorrect.
A few students also neglect to cancel the principal P early, which can make the equation look more complicated than it actually is.

Final Answer:
The required simple interest rate is 12.5 percent per annum.