Question

the compound interest on Rs.40000 5% pa and 4 years is​

Answer 1

$\bf \: \underline{ Given }\: :$ ↴

$\sf \: Principal \: : \: Rs. \: 40000$

$\sf \: Rate \: of \: Interest \: : \: 5 \: \%$

$\sf \: Time \: : \: 4\: Years.$

$\bf \: \underline{To \: find }\: :$ ↴

$\sf \: We \: have \: to \: find \: the \: Compound \: Interest.$

$\bf \: \underline{Solution \: } \: :$ ↴

$\sf \: First \: of \: all \: we \: have \: to \: find \: the \: amount.$

${ \underline{\boxed{ \red{ \sf \: Amount \: : P \: \bigg(\: 1 + \frac{R}{100} \: \bigg ) ^{n} }}}}$

$\sf \: \underline{Putting \: the \: values},$

$\sf \: \implies \: 40000 \: \bigg(\: 1 + \dfrac{5}{100} \bigg ) ^{4}$

$\sf \:\implies\: 40000 \: \bigg(\: 1 + \dfrac{1}{20} \bigg ) ^{4}$

$\sf \:\implies\: 40000 \: \bigg(\dfrac{20 + 1}{20} \bigg ) ^{4}$

$\sf \:\implies\: 40000 \: \bigg(\dfrac{21}{20} \bigg ) ^{4}$

$\sf \:\implies\: 40000 \times \dfrac{194481}{160000}$

$\sf \:\implies\: \dfrac{194481}{4}$

$\sf \:\implies\: 48620.25$

$\sf \: \pink{Thus, \: amount =Rs. \: 48620.25 }$

$\sf \: \underline{Now, we \: will \: find \: the \: Compound \: Interest.}$

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

$\sf \: \underline{Putting \: the \: values},$

${ \sf {CI = 48620.25\: - \: 40000}}$

$\underline{ \boxed{ \purple{{ \sf {CI = Rs. \: 8620.25}}}}}$

Answer 2

Answer:

$\begin{gathered}\large\begin{gathered}\begin{gathered}\begin{gathered} \dag\: \bf\red {Given :}\begin{cases} &\sf{Principle = Rs.40000} \\ &\sf{{Rate = 5 \: \%}}\\ &\sf{{Time = 4 \: years}} \end{cases}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered} \\ \end{gathered}$

$\begin{gathered}\large\begin{gathered}\begin{gathered}\begin{gathered} \dag\: \bf\red {To \: Find :} \begin{cases} &\sf{Compound \: Interest } \end{cases}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\begin{gathered} \\ \end{gathered}$

$\large{\dag \: \bf\red{Using \: Formulae : }}$

$\begin{gathered} \\ \end{gathered}$

${\bigstar{\underline{\boxed{\sf \: Amount \: : P \: \bigg(\: 1 + \frac{R}{100} \: \bigg ) ^{n}}}}}$

$\begin{gathered} \\ \end{gathered}$

${\bigstar{\boxed{\sf{Compound \: Interest = Amount- Principal}}}}$

$\begin{gathered} \\ \end{gathered}$

$\large {\dag \: {\bf{\red{Solution : }}}}$

$\begin{gathered} \\ \end{gathered}$

${\underline{\pink{\pmb{\frak{Firstly \: Finding \: The \: Amount }}}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{P \: \bigg(\: 1 + \dfrac{R}{100} \: \bigg) ^{n}}}$

$\begin{gathered} \\ \end{gathered}$

• Substituting the values

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{40000 \: \bigg(\: 1 + \dfrac{5}{100} \: \bigg ) ^{4}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{40000 \: \bigg(\: \dfrac{100 + 5}{100} \: \bigg ) ^{4}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{ 40000 \: \bigg(\: \dfrac{105}{100} \: \bigg ) ^{4}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{ 40000 \: \bigg(\: {\cancel\dfrac{105}{100}}\: \bigg ) ^{4}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{40000 \: \bigg(\:\dfrac{21}{20}\: \bigg ) ^{4}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{ 40000 \: \bigg(\dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20}\bigg )}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{ 40000 \: \bigg(\dfrac{194,481}{160,000} \bigg )}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf{ 40000\times \dfrac{194,481}{160,000}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount \: = \bf {\cancel{40000}\times \dfrac{194,481} {\cancel{160,000}}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount=\bf{\dfrac{194,481}{4}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount=\bf {\cancel{\dfrac{194,481}{4}}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies\sf \: Amount=\bf{48,620.25}}$

$\begin{gathered} \\ \end{gathered}$

$\bigstar{\underline{\boxed{\sf{Amount={Rs.48,620.25}}}}}$

$\begin{gathered} \\ \end{gathered}$

$\underline\pink{\pmb{\frak{Now \: Finding \: The \: Compound \: Interest }}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies \: \sf{Compound \: Interest = \bf{Amount- Principal}}}$

$\begin{gathered} \\ \end{gathered}$

• Substituting the values

$\begin{gathered} \\ \end{gathered}$

${: \implies \: \sf{Compound \: Interest = \bf{48,620.25- 40000}}}$

$\begin{gathered} \\ \end{gathered}$

${: \implies \: \sf{Compound \: Interest = \bf 8620.25}}$

$\begin{gathered} \\ \end{gathered}$

${\bigstar{\underline{ \boxed{\sf{Compound \: Interest = 8620.25}}}}}$

$\begin{gathered} \\ \end{gathered}$

• Henceforth,The Compound Interest is Rs.8620.29.

$\begin{gathered} \\ \end{gathered}$

$\large {\dag \: {\bf{\red{Know \: More : }}}}$

Formula of Simple Interest (S.I)

$\begin{gathered} \\ \end{gathered}$

${\boxed{\sf{S.I = \dfrac{P \times R \times T}{100}}}}$

$\begin{gathered} \\ \end{gathered}$

Formula of Principle(P) if Amount and Interest given

$\begin{gathered} \\ \end{gathered}$

★ ${\boxed{\sf{P=Amount - Interest}}}$

$\begin{gathered} \\ \end{gathered}$

Formula of Principle (P) if Interest,time and rate given

$\begin{gathered} \\ \end{gathered}$

★ ${\boxed{\sf{P = \dfrac{Interest \times 100 }{Time \times Rate}}}}$

$\begin{gathered} \\ \end{gathered}$

Formula of Principle (P) if amount,time and rate given

$\begin{gathered} \\ \end{gathered}$

★ ${\boxed{\sf{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}$

$\begin{gathered} \\ \end{gathered}$

Formula of Amount if Principle (P) and Interest (I) given

$\begin{gathered} \\ \end{gathered}$

★ ${\boxed{\sf{Amount = Principle + Interest }}}$