When simple and compound agree — Aptitude Question
When simple and compound agree: For which period are the simple and compound interest on the same sum at the same… Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 50 seconds
Question
For which period are the simple and compound interest on the same sum at the same rate exactly equal?
Options
- 1 year
- 2 years
- 3 years
- They are never equal
Show the answer and the worked solution
Correct answer: A. 1 year
Worked solution
- In the first year interest is charged on the principal alone under both schemes.
- Compounding only begins to differ from the second year, when interest earns interest.
- So they are equal for 1 year.
Answer: 1 year.
The idea
The whole difference between the two schemes is interest on interest. Until a full period has passed there is no accumulated interest to compound, so the two coincide.
Shortcut. Try ₹100 at 10%: both schemes pay ₹10 in year one; in year two compound pays ₹11 against ₹10. The tie holds only for the first period.
Common trap. "They are never equal" — assuming compounding always earns more; it only pulls ahead once there is interest to earn interest, after the first year.
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