Question

Calculate the amount and compound interest : ₹100 for 1 year at 10% per annum compounded half - yearly​

Answer 1

Step-by-step explanation:

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Answer 2

$\sf \large{ \underline{ \underline{\maltese\:Given}} }$

$\implies \sf \: Principal : Rs. \: 100$

$\implies \: \sf Time : 1 \: Year$

$\sf \implies \: Rate : 10 \: \% \: [Compounded \: half \: yearly]$

$\sf\large{ \underline{ \underline{\maltese\:To \: find }} }$

$\sf \implies \: Amount \: and \: compound \: interest = \: ?$

$\sf\large{ \underline{ \underline{\maltese\:Solution }} }$

➢ Note : When interest is compounded half yearly, then rate of interest would be halfed and time (n) will be doubled that is 2n.

$\bf \underline{Now},$

$\implies \sf \: Principal : Rs. \: 100$

$\implies \: \sf Time : 1 \: Year = 1 \times 2 = 2 \: Year$

$\implies \: \sf Rate : \dfrac{10}{2} = 5 \: \%$

$\bf \underline{Now},$

$\sf \implies{ \underline{ \boxed{ \sf \: Amount \: = P \: \left(\: 1 + \dfrac{R}{100} \: \right ) ^{n} }}}$

$\sf Substitute \: the \: values,$

$\sf \implies \sf \: Amount \: = 100 \: \left(\: 1 + \cancel{\dfrac{5}{100}} \: \right)^{2}$

$\sf \implies \sf \: Amount \: = 100 \: \left(\: 1 + \dfrac{1}{20} \: \right)^{2}$

$\sf \implies \sf \: Amount \: = 100 \: \left(\ \dfrac{20 + 1}{20} \: \right)^{2}$

$\sf \implies \sf \: Amount \: = 100 \: \left(\ \dfrac{21}{20} \: \right)^{2}$

$\sf \implies \sf \: Amount \: = \cancel{100} \: \left(\ \dfrac{441} {\cancel{400} }\: \right)$

$\sf \implies \sf \: Amount \: = \: \ \dfrac{441} {4} \:$

$\sf \implies \sf \: Amount \: = \: Rs. \: 1 10.25$

$\sf \implies \sf \: \underline{\boxed{ \sf Therefore, \: the \: amount \: is \: Rs. \: 110.25 }}\: \bigstar$

$\bf \underline{Now},$

$\sf \implies{ \underline{ \boxed{ \sf \: Compound \: interest = Amount - Principal }}}$

$\sf \implies{ \sf \: Compound \: interest = Rs.( 110.25 - 100) }$

$\sf \implies{ \sf \: Compound \: interest = Rs. \: 10.25 }$

$\sf \implies \sf \: \underline{\boxed{ \sf Therefore, \: the \:compound \: interest \: is \: Rs. \: 10.25 }} \: \bigstar$