Rate changing over the years — Aptitude Question
Rate changing over the years: A sum of ₹10,000 earns simple interest at 5% for the first 2 years, 8% for the next 3… Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
A sum of ₹10,000 earns simple interest at 5% for the first 2 years, 8% for the next 3 years and 10% thereafter. What is the total interest after 7 years?
Options
- ₹5,400
- ₹5,600
- ₹5,800
- ₹6,000
Show the answer and the worked solution
Correct answer: A. ₹5,400
Worked solution
- First 2 years: 10,000 × 5 × 2/100 = ₹1,000.
- Next 3 years: 10,000 × 8 × 3/100 = ₹2,400.
- Last 2 years: 10,000 × 10 × 2/100 = ₹2,000.
- Total = ₹5,400.
Answer: ₹5,400.
The idea
Break the period at each rate change and add. Under simple interest the principal never changes, so each stretch is independent.
Shortcut. Add the rate-years: 5 × 2 + 8 × 3 + 10 × 2 = 54, so the interest is 54% of ₹10,000.
Common trap. ₹5,600 — swapping the stretches, giving 8% two years and 10% three (10 + 16 + 30 = 56%); 'thereafter' covers only years 6 and 7.
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