Question

Calculate the amount and compound on 6250 for 1 year at 16% per annum compounded half yearly​

Answer 1

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

$\implies \sf \: Principal : Rs. \: 6250$

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

$\sf \implies \: Rate : 16 \% \: \: [Compounded \: half \: yearly]$

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

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

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

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

$\small{\bf Now, }$

$\implies \sf \: Principal : Rs. \: 6250$

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

$\sf\implies Rate : \dfrac{16}{2} = 8 \%$

$\small{\bf Now, }$

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

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

$\sf \implies \sf \: Amount \: = 6250 \: \left(\: 1 + \cancel{\dfrac{8}{100}} \: \right)^{2}$

$\sf \implies \sf \: Amount \: = 6250 \: \left(\: 1 + {\dfrac{2}{25}} \: \right)^{2}$

$\sf \implies \sf \: Amount \: = 6250 \: \left(\:{\dfrac{25 + 2}{25}} \: \right)^{2}$

$\sf \implies \sf \: Amount \: = 6250 \: \left(\:{\dfrac{27}{25}} \: \right)^{2}$

$\sf \implies \sf \: Amount \: = \cancel{6250 }\: \left(\:{\dfrac{729}{ \cancel{625}} }\: \right)$

$\sf \implies \sf \: Amount \: = 10 \times 729$

$\sf \implies \sf \: Amount \: =Rs. \: 7290$

$\sf \implies \sf \: \underline{\boxed{ \sf Therefore, \: the \: amount \: is \: Rs. \: 7290 }}\: \bigstar$

$\small{\bf Now, }$

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

$\sf \implies{ \sf \: Compound \: interest = Rs.( 7290 - 6250) }$

$\sf \implies{ \sf \: Compound \: interest = Rs. \: 1040}$

$\sf \implies \sf \: \underline{\boxed{ \sf Therefore, \: the \:compound \: interest \: is \:Rs.\:1040}}\:\bigstar$