Simple Interest – Time to quadruple when doubling time is known: If a certain sum doubles itself in 8 years at simple interest, in how many years will it become four times the principal?
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: 24 years
Explanation
Introduction / Context:In simple interest, growth is linear with time. If we know the time to double, we can scale proportionally to find the time to quadruple the principal.
Given Data / Assumptions:
- Doubling time t2 = 8 years
- Simple interest model
Concept / Approach:Doubling at SI means interest equals P over 8 years, so r = 1 / 8 = 12.5% per annum. For quadrupling (A = 4P), interest must be 3P, so time t4 = 3P / (P * r) = 3 / r.
Step-by-Step Solution:
From doubling: r = 1 / 8 = 0.125 = 12.5%For A = 4P: required interest = 3Pt = 3P / (P * 0.125) = 3 / 0.125 = 24 yearsVerification / Alternative check:
Linear scaling: Doubling needs 8 years; quadrupling needs twice the gain (from +P to +3P is 3 times P vs 1P), but relative to zero it is threefold interest. Time = 3 * 8 / 1? Using r is clearer; result 24 years.Why Other Options Are Wrong:
- 16/12/20 years: inconsistent with r = 12.5%.
- 32 years: overestimates required time.
Common Pitfalls:
- Treating the process as compounding.
- Confusing quadruple of P with four times the interest.
Final Answer:24 years.