From one year's amount to the next — Aptitude Question
From one year's amount to the next: A sum at compound interest amounts to ₹4,410 in 2 years and ₹4,630.50 in 3 years. Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A sum at compound interest amounts to ₹4,410 in 2 years and ₹4,630.50 in 3 years. What is the rate of interest?
Options
- 4%
- 5%
- 6%
- 7%
Show the answer and the worked solution
Correct answer: B. 5%
Worked solution
- Interest for the third year = 4,630.50 − 4,410 = ₹220.50.
- This is one year's interest on ₹4,410.
- Rate = 220.50 / 4,410 × 100 = 5%.
Answer: 5%.
The idea
Consecutive amounts differ by exactly one year's interest on the earlier amount. That single division gives the rate without ever finding the principal.
Shortcut. 4,410 = 4,000 × 1.05², a recognisable 5% amount; 5% of 4,410 is 220.50, which confirms it at once.
Common trap. 6% — treating it as simple interest: ₹220.50 a year puts the principal at 4,410 − 441 = ₹3,969, and 220.50 ÷ 3,969 ≈ 5.6%.
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