Question

calculate the compound interest on ₹12000 for 2 years at 20% per annum when compounded half yearly.​

Answer 1

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

• Calculate the compound interest on ₹12000 for 2 years at 20% per annum when compounded half yearly.

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

• Principal (p)= $\sf\green{Rs.12000}$
• Rate (r)= $\sf\green{ 20\%}$
• Time (n) = $\sf\green{2 years}$

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

Amount after 2 years =

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:\qquad \bull \: { \sf{Amount \: }= \bf P \bigg(1 + \dfrac{R}{200}\bigg)}^{2n} }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\:\: to \:\:the\:\: Formula:}} \\\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow { \sf{Amount \: }= \bf 12000 \bigg(1 + \dfrac{2 \cancel0 }{20 \cancel0 }\bigg)}^{2 \times 2}$

$\qquad \quad {:} \longrightarrow { \sf{Amount \: }= \bf 12000 \bigg(1 + \dfrac{1 }{10}\bigg)}^{4}$

$\qquad \quad {:} \longrightarrow { \sf{Amount \: }= \bf 12000 \bigg(\dfrac{11 }{10}\bigg)}^{4}$

$amount \: = \: \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10} \times \frac{11}{10}$

$\qquad \quad {:} \longrightarrow { \sf{Amount \: }= \bf 12 \cancel0 \cancel0 \cancel0 \: \: \: \: \times \: \frac{14641}{10 \cancel0 \cancel0 \cancel0} }$

$\qquad\quad {:} \longrightarrow \underline {\boxed{\sf{Amount = ₹17569.20 }}}$

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$\boxed{ \sf \red{ CI\: = \: Amount\:- \: Principal }}$

$\qquad \quad {:} \longrightarrow \: 17569.20 \: - \: 12000$

$\begin{gathered}\qquad \therefore\: \sf{ Compound \: Interest= \underline {\underline{₹5569.20 }}}\\\end{gathered}$

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