Simple Interest – Rate percent when a sum trebles: A sum of money placed at simple interest becomes three times the principal in 15 years. Find the annual rate of interest (percent per annum).
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: 13 1/3%
Explanation
Introduction / Context:Trebles means the amount equals 3P, so the interest earned is 2P. With SI, SI = P * r * t; solve for r using t = 15 years.
Given Data / Assumptions:
- A = 3P
- t = 15 years
Concept / Approach:Since SI = A - P = 2P, we have P * r * 15 = 2P ⇒ r = 2 / 15 per year = 0.1333... = 13 1/3%.
Step-by-Step Solution:
r = 2 / 15 = 0.1333... = 13 1/3%Verification / Alternative check:
A = P * (1 + r * t) = P * (1 + 2) = 3P (consistent)Why Other Options Are Wrong:
- 16 2/3% / 12 2/3% / 20% / 10%: do not equal 2 / 15 as a percent.
Common Pitfalls:
- Confusing treble (3P) with double (2P).
Final Answer:13 1/3% per annum.