CAPF AC 2022 Q4: General Mental Ability – Quantitative Aptitude
- (a) 10%
- (b) 10.5%
- (c) 11%
- (d) 12%
Answer: (b) 10.5%
Explanation
Simple interest rate equal to compound interest
Given: a bank pays 10% per annum compounded annually for two years; find the simple interest rate per annum that gives the same maturity amount.
How to think: find what ₹100 becomes in two years with compounding.
Then spread that total interest equally over two years.
| Step | Working |
|---|---|
| After year 1 | 100 × 1.10 = ₹110 |
| After year 2 | 110 × 1.10 = ₹121 |
| Total interest | ₹21 on ₹100 in 2 years |
| Simple rate per year | 21 ÷ 2 = 10.5% |
Why it is more than 10%: in the second year, interest is also earned on the first year's interest of ₹10.
That extra ₹1 raises the average rate by half a per cent.
Answer: (b) 10.5%.
Why each option is right or wrong
- (a) Incorrect. 10% simple interest gives only ₹120, not ₹121.
- (b) CORRECT. ₹21 of interest over two years is 10.5% a year.
- (c) Incorrect. 11% simple interest would give ₹122.
- (d) Incorrect. 12% simple interest would give ₹124.
Key point
Compound amount = P(1 + r)ⁿ. At 10% for 2 years ₹100 becomes ₹121. Equivalent simple rate = total interest ÷ years = 10.5%.
Remember
10% compounded for 2 years = 21% = 10.5% simple.
Common mistakes
- Saying 10% because the rate is the same, ignoring interest on interest.
- Giving the two-year total of 21% as the rate per annum.
- Using the three-year figure of 33.1% by miscounting the period.
Exam tip
Educated guess: compound interest always beats simple interest at the same rate, so the answer is slightly above 10%. The extra is only ₹1 on ₹100 over two years, which is half a per cent a year.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (compound interest)
- R. S. Aggarwal, Quantitative Aptitude — Simple Interest and Compound Interest