Consider the compound interest in the following cases:
(A) The compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs. 2500
(B) The compound interest on Rs 2800 at 10% per annum for 18 months is Rs. 434.
Choose the correct statment(s):e correct statment(s):
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Only (B)
Let’s check each statement.
(A)
Principal = ₹16000
Rate = 20% p.a. ⇒ 5% per quarter
Time = 9 months = 3 quarters
$\text{Amount} = 16000(1.05)^3 = 16000 \times 1.157625 = ₹18522$
$\text{CI} = 18522 - 16000 = ₹2522 \neq ₹2500$
Statement (A) is incorrect
(B)
Principal = ₹2800
Rate = 10% p.a.
Time = 18 months = $1\frac{1}{2}$ years
For annual compounding:
- After 1 year:
$2800 \times 1.10 = 3080$
- Simple interest for next 6 months:
$3080 \times 10\% \times \frac{1}{2} = 154$
Final amount = 3080 + 154 = 3234
$\text{CI} = 3234 - 2800 = ₹434$
Statement (B) is correct