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Find the compound interest on $Rs\,32000$ at 20% per annum for 1 year, compounded half yearly.
A. 6320
B. 6720
C. 6400
D. 6500

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Last updated date: 19th Jul 2024
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Answer
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Hint: To find the compound interest, we have been given with principal, rate of interest and time, on using the formula we can easily find the compound interest.

Complete step-by-step answer:
Principal (P) = $Rs.32000$
$Rate\,R = 20\% \,per\,annum$
Since it is compounded half yearly , the rate of interest is considered for the half yearly period.
Therefore,
Rate (R) = $\dfrac{{20\% }}{2} = 10\% \,per\,half\,year$
Time (T) is 1 year = 2 half-year
$Amount = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
On putting the values, we get,
$Amount = 32000\left( {\dfrac{{121}}{{100}}} \right)$
Therefore, when we solve it we get,
Amount = 38720
We know that, Interest = Amount – Principal, we already have the value of amount and principle, on putting the values in the formula, we get,
Interest = 38720 - 32000
Interest = Rs.6720

Note: While applying the formula take note of the time as in this question it has been given that the amount is compounded half yearly.