Question : What is the interest payable on INR 12,000 for 3 months at the rate of 10% per annum, if interest is compounded quarterly?
Option 1: INR 250
Option 2: INR 200
Option 3: INR 300
Option 4: INR 350
Correct Answer: INR 300
Solution :
Principal Amount (P) = INR 12000
Time (T) = 3 months
Rate of Interest (R) = 10% per annum
The amount borrowed is compounded quarterly
Time = 3 months = $\frac{3}{12} = \frac{1}{4}$ years
For quarterly, the rates are divided by 4, and time is multiplied by 4
Quarterly rates = $\frac{10}{4} = \frac{5}{2}$%
New Time = $\frac{1}{4}\times 4$ = 1 quarter
Amount = $\text{P}\times (1+\frac{\text{R}}{100})^{\text{T}} = 12000\times(1+\frac{\frac{5}{2}}{100})^1 = 12000\times \frac{41}{40}$
= 300 × 41 = INR 12300
Compound interest = Amount – Principal = INR 12300 – INR 12000 = INR 300
$\therefore$ The compound Interest payable at compounded quarterly is INR 300
Hence, the correct answer is INR 300.
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