Question

find the compound interest on Rs 1000 at rate of 10% per annum for 18 months when interest is compounded half yearly​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• Find the compound interest on Rs 1000 at rate of 10% per annum for 18 months when interest is compounded half yearly

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

• Principal ( P ) = $\sf\green{ Rs,1000}$
• Rate ( R ) = $\sf\green{ 10\%\: per \: annum}$
• Time ( n ) = $\frac{18}{12 } \: = \:$ $\sf\green{ \frac{3}{2} }$

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

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Amount \: after \: 18 \: Months \: = \: P \bigg(1 + \frac{R}{200} \bigg) ^{2n} }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 1000\: \times \: \bigg(1 + \frac{10}{200} \bigg) ^{2 \times \frac{3}{2} } }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 1000 \: \times \: \bigg(1 + \frac{1 \cancel0}{20 \cancel0} \bigg) ^{ \cancel2 \times \frac{3}{ \cancel2} } }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 1000 \: \times \: \bigg(1 + \frac{1}{20} \bigg) ^{3 } }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 1000 \: \times \: \bigg( \frac{21}{20} \bigg) ^{3 } }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 1000 \: \times \: \bigg( \frac{21}{20} \bigg) \times \bigg( \frac{21}{20} \bigg) \times \bigg( \frac{21}{20} \bigg) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 1 \cancel{000} \: \times \: \frac{21}{2 \cancel0} \times \frac{21}{2 \cancel0} \times \frac{21}{2 \cancel0} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 1 \: \times \: \frac{21}{2 } \times \frac{21}{2 } \times \frac{21}{2 } }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \frac{9261}{8} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \cancel\green{\frac{9261}{8}} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ \:Amount \: after \: 18 \: Months \: = \: Rs,1157.63 }}}$

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$\underbrace\orange{\boxed{ \sf \blue{ Compound \: Interest}}}$

$\quad {:} \longrightarrow \sf{\sf{ Compound \: interest \: = \: Amount \: - \: Principal }}$

$\quad {:} \longrightarrow \sf{\sf{ Compound \: interest \: = \: 1157.63 \: - \: 1000 }}$

$\quad {:} \longrightarrow \sf{\sf{ Compound \: interest \: = \: Rs,157.63 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{ Compound \: interest \: = \: Rs,157.63}}}$

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More For Knowledge :-

$\boxed{\begin{minipage}{5cm}\bigstar \:\underline{\textbf{Profit and Loss Formulas :}}\\\\ \\ \sf {\textcircled{\footnotesize\textsf{1}}} \:S.P. = \sf \bigg\lgroup\dfrac{100 + Profit \%}{100}\bigg\rgroup \times 100 \\\\\\ \sf {\textcircled{\footnotesize\textsf{2}}} \:\:C.P. = \sf \dfrac{S.P. \times 100}{100 + Profit \%} \\\\\\\sf{\textcircled{\footnotesize\textsf{3}}} \:\:Profit = \sf \dfrac{Profit \% \times C.P.}{100} \\\\\\ \sf{\textcircled{\footnotesize\textsf{4}}} \: \:Profit (gain) = S.P. - C.P. \\\\\\\sf{\textcircled{\footnotesize\textsf{5}}} \: \: \sf Profit \% = \dfrac{Profit}{C.P.} \times 100 \end{minipage}}$

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