Question

find the compound interest on ₹32000 for 1 year at the rate of 20% per annum if the interest is compounded quarterly.​

Answer 1

Answer:

Principal (P) = ₹ 32,000

Time (t) = 1 Year

Rate (r) = 20%

Amount = Principal × (1 + (r/2 × 100)) n × 2

= ₹ 32,000 × (1 + (20/200)) 1 × 2

= ₹ 32,000 × (11/10)2

= ₹ 32,000 × 11/10 × 11/10

= ₹ 38,720

C.I. = Amount – Principal

= ₹ 38,720 - ₹ 32,000 = ₹ 6,720

Answer 2

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

• Find the compound interest on ₹32000 for 1 year at the rate of 20% per annum if the interest is compounded quarterly.

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

• $\bf \: Principal \: = \: { \boxed{Rs,32000}}$
• $\bf \: Rate \: = \: { \boxed{20\%}}$
• $\bf \: Time \: = \: { \boxed{1\: Year}}$

$\red{\boxed{ \sf \blue{ The \: Interest \: is\: Compounded\: Quarterly }}}$

$\large\underline{ \underline{ \sf \maltese{ \: </strong><strong>Solution</strong><strong>:- }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Amount \: = \: Principal \: \bigg(1 \: + \: \frac{Rate}{400} \bigg)^{4n} }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\bf{ Amount \: after \: 1 \: Year \: = \: Principal \: \bigg(1 \: + \: \frac{Rate}{400} \bigg)^{4n} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: 32000 \: \bigg(1 \: + \: \frac{20}{400} \bigg)^{4\: \times \: 1} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: 32000 \: \bigg(1 \: + \: \frac{ \cancel \green2 \cancel0}{ \cancel \green{40} \cancel0} \bigg)^{4\: \times \: 1} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: 32000 \: \bigg(1 \: + \: \frac{ 1}{20} \bigg)^{4} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: 32000 \: \times \: \: \bigg( \frac{ 21}{20} \bigg)^{4} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: 32000 \: \times \: \: \bigg( \frac{ 21}{20} \bigg) \times \bigg( \frac{ 21}{20} \bigg) \times \bigg( \frac{ 21}{20} \bigg) \times \bigg( \frac{ 21}{20} \bigg)}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: 32000 \: \times \: \: \frac{ 21}{20} \times \frac{ 21}{20} \times \frac{ 21}{20} \times \frac{ 21}{20} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: 32 \cancel{000} \: \times \: \: \frac{ 21}{2 \cancel0} \times \frac{ 21}{2 \cancel0} \times \frac{ 21}{2 \cancel0} \times \frac{ 21}{20} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: 32\: \times \: \: \frac{ 21}{2 } \times \frac{ 21}{2 } \times \frac{ 21}{2 } \times \frac{ 21}{20} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: \frac{ 32 \: \times \: 21 \: \times \: 21 \: \times \: 21 \: \times \: 21}{2 \: \times \: 2 \: \times \: 2 \: \times \: 20} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: \frac{6223392}{160} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ Amount \: = \: \cancel\frac{6223392}{160} }}$

$\qquad \quad {:} \longrightarrow \sf{\bf{ Amount \: after \: 1 \: Year \: = \: Rs, 38896.2 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Amount \: = \: Rs, 38896.2 }}}$

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$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Compound \: Interest \: = \: Amount \: - \: Principal }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Compound \: Interest \: = \: 38896.2 \: - \: 32000 }}$

$\qquad \quad {:} \longrightarrow \sf{\bf{Compound \: Interest \: = \: 6896.2 }}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Compound\: Interest \: = \underline {\underline{ Rs,6896.2}}}\\\end{gathered}\end{gathered}$

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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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