Principal from ₹9,261 in three years — Aptitude Question
Principal from ₹9,261 in three years: A sum amounts to ₹9,261 in 3 years at 5% per annum compound interest. Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A sum amounts to ₹9,261 in 3 years at 5% per annum compound interest. What was the principal?
Options
- ₹7,500
- ₹8,000
- ₹8,400
- ₹8,500
Show the answer and the worked solution
Correct answer: B. ₹8,000
Worked solution
- 1.05³ = 1.157625.
- P = 9,261 ÷ 1.157625 = ₹8,000.
- Check: 8,000 → 8,400 → 8,820 → 9,261. ✓
Answer: ₹8,000.
The idea
Present value = amount ÷ (1 + r)ⁿ. Stepping the years forward from the answer is the fastest way to confirm it.
Shortcut. 9,261 is 21³ and 1.05 is 21/20, so the principal is 20³ = ₹8,000.
Common trap. ₹8,400 — dividing by 1.05 only twice (9,261 ÷ 1.1025); three years means three divisions, and ₹8,400 is the amount after the first year.
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