Question : What will be the compound interest on Rs. 21000 at the rate of 10% per annum for 6 months compounded half-yearly?
Option 1: Rs. 1680
Option 2: Rs. 1050
Option 3: Rs. 1850
Option 4: Rs. 1250
Correct Answer: Rs. 1050
Solution :
The formula for the calculation of compound interest for half a year,
$\text{Compound interest}=\text{Principal}×(1+\frac{\text{Rate}}{2×100})^{\text{2×Time}}-\text{Principal}$
$⇒\text{Compound interest}=21000×(1+\frac{\text{10}}{2×100})^{\text{2×0.5}}-21000$
$⇒\text{Compound interest}=21000×(1+\frac{\text{1}}{20})^{\text{1}}-21000$
$⇒\text{Compound interest}=21000×(\frac{\text{21}}{20})-21000$
$⇒\text{Compound interest}=22050-21000$
$\therefore\text{Compound interest}=1050$
Hence, the correct answer is Rs. 1050.
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