Question

[tex]{\huge{\fbox{\color{purple}{Question :-}}}}
Find the amount and the compound interest on 5000 for 2 years at 6% per annum, interest payable yearly.​

Answer 1

$\bf \huge \mapsto \: Given:$

$\bf \small \implies \: Principal \: (P) \: = \: 5000$

$\bf \small \implies \:Rate \: \: of \: \: interest (r) \: = \: 6% p.a.$

$\bf \implies \: Time \: \: Period (n) = \: 2 \: \: years$

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$\bf \huge \mapsto \: To \: \: Find :$

Compound interest on 5000 for 2 years at 6% per annum, interest payable yearly.

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$\bf \huge \mapsto \: Solution :$

$\bf \implies \: We \: \: \: already \: \: \: Know \: \: \: that$

$\bf \large\implies \: Amount \: = P \: ( \: \frac{1 + r}{100} \: )^{n}$

⇨ Putting the values ,

$\bf \large\implies \: \: 5000 \: \: ( \: \frac{1 \: + \: 6}{100} \: ) \:^{2}$

$\bf \large\implies \: 5000 \: \: ( \: \frac{106}{100} \: ) \:^{2}$

$\bf \large\implies \: 5000 \times \frac{53}{50} \times \frac{53}{50}$

$\bf \large\implies \: \: 5618$

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☛ After that ,

$\bf \mapsto \: We \: \: know \: \: that ,$

$\:$

Compound interest = Amount - Principal

$\large \leadsto \: 5618−5000 \\ \\ \large \leadsto \: 618$

Answer 2

Answer:

${\Large{\pmb{\sf{\underline{\underline{Given...}}}}}}$

• $\leadsto$ Principle = Rs.5000
• $\leadsto$ Time = 2 years
• $\leadsto$ Rate of Interest = 6%

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

${\Large{\pmb{\sf{\underline{\underline{To \: Find...}}}}}}$

• $\leadsto$ Amount
• $\leadsto$ Compound Interest

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

${\Large{\pmb{\sf{\underline{\underline{Using \: Formulas...}}}}}}$

$\quad{\dag{\underline{\boxed{\sf{Amount ={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}}$

$\quad\dag{\underline{\boxed{\sf{Compound \: Interest = Amount- Principle }}}}$

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

${\Large{\pmb{\sf{\underline{\underline{Solution...}}}}}}$

${\bigstar \:{\underline{\pmb{\frak{\green{Firstly, calculating\: the \: Amount }}}}}}$

$\quad {\longmapsto{\sf{Amount = {P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}$

• Substituting the values

$\quad {\longmapsto{\sf{Amount = {5000{\bigg(1 + \dfrac{6}{100}{\bigg)}^{2}}}}}}$

$\quad {\longmapsto{\sf{Amount = {5000{\bigg(\dfrac{(1 \times 100) + 6}{100}{\bigg)}^{2}}}}}}$

$\quad {\longmapsto{\sf{Amount = {5000{\bigg(\dfrac{100 + 6}{100}{\bigg)}^{2}}}}}}$

$\quad {\longmapsto{\sf{Amount = {5000{\bigg(\dfrac{106}{100}{\bigg)}^{2}}}}}}$

$\quad {\longmapsto{\sf{Amount = {5000{\bigg({\cancel{\dfrac{106}{100}}}{\bigg)}^{2}}}}}}$

$\quad {\longmapsto{\sf{Amount = {5000{\bigg(\dfrac{53}{50}{\bigg)}^{2}}}}}}$

$\quad {\longmapsto{\sf{Amount = {5000{\bigg(\dfrac{53}{50} \times \dfrac{53}{50}{\bigg)}}}}}}$

$\quad {\longmapsto{\sf{Amount = {5000{\bigg(\dfrac{2809}{2500}{\bigg)}}}}}}$

$\quad {\longmapsto{\sf{Amount = {5000 \times \dfrac{2809}{2500}}}}}$

$\quad {\longmapsto{\sf{Amount = {\cancel{5000} \times \dfrac{2809}{\cancel{2500}}}}}}$

$\quad {\longmapsto{\sf{Amount = {2 \times {2809}}}}}$

$\quad {\longmapsto{\sf{Amount = {Rs.5618}}}}$

$\quad{\dag{\underline{\boxed{\sf{\pink{Amount = {Rs.5618}}}}}}}$

$\therefore{\sf{\underline{\underline{\red{The \: Amount \: is \: Rs.5618}}}}}$

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

${\bigstar \:{\underline{\pmb{\frak{\green{Now,Finding \: the \: Compound \: Interest}}}}}}$

$\quad{ \longmapsto{\sf{Compound \: Interest = {Amount - Principle }}}}$

• Substituting the values

$\quad{ \longmapsto{\sf{Compound \: Interest = {5681 - 5000}}}}$

$\quad{ \longmapsto{\sf{Compound \: Interest = {Rs.618}}}}$

$\quad{\dag{\underline{\boxed{\sf{\pink{Compound \: Interest = {Rs.618}}}}}}}$

$\therefore{\sf{\underline{\underline{\red{The \: Compound \: Interest \: is \: Rs.618}}}}}$

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

${\Large{\pmb{\sf{\underline{\underline{Learn \: More...}}}}}}$

$\quad\circ{\underline{\boxed{\sf{\blue{A ={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}}$

$\quad\circ{\underline{\boxed{\sf{\blue{Amount = Principle + Interest}}}}}$

$\quad\circ{\underline{\boxed{\sf{\blue{ P=Amount - Interest }}}}}$

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

$\quad\circ{\underline{\boxed{\sf{\blue{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}}}}}}$

$\quad\circ{\underline{\boxed{\sf{\blue{P = \dfrac{Interest \times 100 }{Time \times Rate}}}}}}$