Simple Interest Rate for Doubling in a Given Time: An amount becomes double of itself in 15 years at simple interest. What is the annual rate of simple interest (in % per annum)?

Introduction / Context:
This question tests your understanding of how simple interest causes an amount to grow over time. You are told that an investment doubles in 15 years under simple interest and asked to find the annual rate of simple interest. Doubling-time questions are very common in aptitude exams and often have neat fractional answers.

Given Data / Assumptions:

• Initial principal = P.
• Amount after 15 years = 2P (doubles).
• Time t = 15 years.
• Simple interest is used at a constant annual rate r%.

Concept / Approach:
Under simple interest, total interest I over t years is I = (P * r * t) / 100. If the amount doubles in t years, then the total interest equals the original principal: P + I = 2P, so I = P. This gives a direct equation relating r and t, which you can solve quickly. Then convert the resulting fraction into a percentage and match it to the options.

Step-by-Step Solution:
Step 1: Amount doubles in 15 years, so final amount A = 2P. Step 2: Total interest I = A − P = 2P − P = P. Step 3: Use the SI formula: I = (P * r * t) / 100. Step 4: Substitute I = P and t = 15: P = (P * r * 15) / 100. Step 5: Cancel P on both sides (P ≠ 0): 1 = (r * 15) / 100. Step 6: Rearrange to solve for r: r = 100 / 15. Step 7: Compute r: 100 / 15 = 6.666..., which is approximately 6.66% per annum. Step 8: Therefore, the annual simple interest rate is about 6.66%.

Verification / Alternative check:
Check by substituting r ≈ 6.66% back into the SI formula. SI for 15 years = (P * 6.66 * 15) / 100 ≈ P * (99.9 / 100) ≈ P. So the total amount is P + I ≈ P + P = 2P, confirming the doubling condition. The slight approximation arises from rounding 6.666... to 6.66%, but for aptitude purposes, this is accurate enough.

Why Other Options Are Wrong:

• 7.85%, 9.41%: Both are higher than needed and would cause the amount to more than double in 15 years.
• 4.21% and 5.00%: These are lower than required and would not be enough to double the amount in 15 years under simple interest.

Common Pitfalls:
Some students mistakenly use the compound interest doubling rule or apply logarithms unnecessarily. Others divide time by 2 instead of linking interest to the principal. Under simple interest, doubling simply means interest equals the principal over the given time, leading directly to the relation r = 100 / t. Keep this shortcut in mind for quick mental calculations.

Final Answer:
The annual rate of simple interest is approximately 6.66% per annum.