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# Calculate compound interest for Rs 10,000 for 1 year at 8% compounded semi – annually.(a) 817(b) 816(c) 815(d) None of these Verified
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Hint: The amount for a principal amount of Rs P for n years and at r% compound interest is given by the formula A = $P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$. The compound interest can be found by subtracting the principal amount from the total amount. If it is required to find the amount for a principal amount of Rs P for n years and at r% per annum compounded semi – annually, then we have to convert the rate r and t in terms of half years and then only we can substitute them in the above formula.

In compound interest, the amount for a principal amount of Rs P for n years and at r% compound interest is given by the formula A = $P{{\left( 1+\dfrac{r}{100} \right)}^{n}}.................\left( 1 \right)$.
To find the compound interest, we will subtract the principal amount from this amount. $.................\left( 2 \right)$
Substituting P = 10000, r = 4, n = 2 in the formula $\left( 1 \right)$, we get,
\begin{align} & A=10000{{\left( 1+\dfrac{4}{100} \right)}^{2}} \\ & \Rightarrow A=10000{{\left( \dfrac{100+4}{100} \right)}^{2}} \\ & \Rightarrow A=10000{{\left( \dfrac{104}{100} \right)}^{2}} \\ & \Rightarrow A=10000\left( \dfrac{10816}{10000} \right) \\ & \Rightarrow A=10816 \\ \end{align}
From $\left( 2 \right)$, the compound interest = Amount – Principal amount
$\Rightarrow$ compound interest = 10816 – 10000
$\Rightarrow$ compound interest = 816