Question : A person borrowed Rs. 8000 on compound interest at the rate of 20% per annum. If the interest is compounded half-yearly, then what will be the amount to be paid after 1.5 years?
Option 1: Rs. 10,648
Option 2: Rs. 11,488
Option 3: Rs. 10,825
Option 4: Rs. 9,865
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Correct Answer: Rs. 10,648
Solution :
Here, Principal = Rs. 8,000
Rate = 20%, but it compounded half-yearly. so, rate = $\frac{20}{2}$ = 10%
since interest is compounded half-yearly, time = 1.5 × 2 = 3
$\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒\text{Total Amount} = 8000 \left(1 + \frac{10}{100}\right)^{3} $
$⇒\text{Total Amount}=8000(\frac{11}{10})^3$
$⇒\text{Total Amount}=8000(\frac{1331}{1000})$
$\therefore \text{Total Amount}=10648 $
Hence, the correct answer is Rs. 10,648.
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