Question : What is the compound interest for 1 year on a sum of Rs. 18000 at the annual rate of 20% per annum compounding half-yearly?
Option 1: Rs. 3780
Option 2: Rs. 2450
Option 3: Rs. 4500
Option 4: Rs. 3650
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Correct Answer: Rs. 3780
Solution :
Given: Principal = Rs. 18000
Rate = 20%, as the interest is half-yearly. so, rate = $\frac{20}{2}$ = 10%
Time = 1 year, as the interest is half yearly so, time = 1 × 2 = 2 years
$\text{Total Amount}$
$=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$ = 18000(1+\frac{10}{100})^2$
$= 18000\times\frac{11}{10}\times\frac{11}{10}$
$= 18000\times\frac{11}{10}\times\frac{11}{10}$
$= 21780$
Now, Compound interest = Total amount – Principal = 21780 – 18000 = Rs. 3780
Hence, the correct answer is Rs. 3780.
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