Question

$\begin{gathered}{\Huge{\textsf{\textbf{\underline{\underline{\color{purple}{Question:}}}}}}}\end{gathered}$

$\begin{gathered}\textsf{Calculate the amount and the compound interest}\\ \ \textsf \ \textsf{on 15000 in 2 years when the rates} \\ \textsf{of interest for successive years are 10 \% }\\ \textsf{and 15 \% respectively.} \end{gathered}$
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Answer 1

Answer:

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{red}{Given:}}}}}}}\end{gathered}$

• $\red\bigstar$ Principle = Rs.15000
• $\red\bigstar$ Time = 2 years
• $\red\bigstar$ Rate of Interests = 10%, 15%

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{red}{To Find:}}}}}}}\end{gathered}$

• $\red\bigstar$ Amount
• $\red\bigstar$ Compound Interest

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{red}{Using Formulae:}}}}}}}\end{gathered}$

$\begin{gathered}\bigstar{\underline{\boxed{\sf {\purple{A =P\bigg\lgroup{1 +\dfrac{R_1}{100} }\bigg\rgroup\bigg\lgroup{1 + \dfrac{R_2}{100}}\bigg\rgroup}}}}} \end{gathered}$

• $\green\star$ A = Amount
• $\green\star$ P = Principle
• $\green\star$ $\sf{R_1}$ = Rate Interest of first year
• $\green\star$ $\sf{R_2}$ = Rate Interest of second year

$\bigstar{\underline{\boxed{\sf{\purple{C.I = \big\lgroup{A - P \big\rgroup}}}}}}$

• $\green\star$ C.I = Compound Interest
• $\green\star$ A = Amount
• $\green\star$ P = Principle

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{red}{Solution:}}}}}}}\end{gathered}$

$\color{green}{\dag \: {\underline{\underline{\frak{Finding \: the \: Amount : }}}}}$

$\quad{: \implies{\sf{A = \bf{P\bigg\lgroup{1 +\dfrac{R_1}{100} }\bigg\rgroup\bigg\lgroup{1 + \dfrac{R_2}{100}}\bigg\rgroup}}}}$

• Substituting the values

$\quad{: \implies{\sf{A = \bf{15000\bigg\lgroup{1 +\dfrac{10}{100} }\bigg\rgroup\bigg\lgroup{1 + \dfrac{15}{100}}\bigg\rgroup}}}}$

$\quad{: \implies{\sf{A = \bf{15000\bigg\lgroup{{\dfrac{(1 \times 100) + 10}{100}}\bigg\rgroup\bigg\lgroup{\dfrac{(1 \times 100) + 15}{100}}\bigg\rgroup}}}}}$

$\quad{: \implies{\sf{A = \bf{15000\bigg\lgroup{{\dfrac{100+ 10}{100}}\bigg\rgroup\bigg\lgroup{\dfrac{100+ 15}{100}}\bigg\rgroup}}}}}$

$\quad{: \implies{\sf{A = \bf{15000\bigg\lgroup{{\dfrac{110}{100}}\bigg\rgroup\bigg\lgroup{\dfrac{115}{100}}\bigg\rgroup}}}}}$

$\quad{: \implies{\sf{A = \bf{15000\bigg\lgroup{{\dfrac{110}{100}} \times {\dfrac{115}{100}}\bigg\rgroup}}}}}$

$\quad{: \implies{\sf{A = \bf{15000\bigg\lgroup{{\dfrac{12650}{10000}}\bigg\rgroup}}}}}$

$\quad{: \implies{\sf{A = \bf{15000 \times {\dfrac{12650}{10000}}}}}}$

$\quad{: \implies{\sf{A = \bf {\cancel{15000}\times{\dfrac{12650}{\cancel{10000}}}}}}}$

$\quad{: \implies{\sf{A = \bf {1.5\times{12650}}}}}$

$\quad{: \implies{\sf{\purple{A = \bf {18975}}}}}$

${\bigstar{\underline{\boxed{\sf{Amount = Rs.18975}}}}}$

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

$\color{green}{\dag \:{\underline{\underline{\frak{Finding \: Compound \: Interest : }}}}}$

$\quad{ : \implies{\sf{C.I = \bf\big\lgroup{A - P \big\rgroup}}}}$

• Substituting the values

$\quad{ : \implies{\sf{C.I = \bf\big\lgroup{18975 - 15000\big\rgroup}}}}$

$\quad{ : \implies{\sf{\purple{C.I = \bf{Rs.3975}}}}}$

${\bigstar{\underline{\boxed{\sf{Compound \: Interest = Rs.3975}}}}}$

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

$\color{green}{\dag \:{\underline{\underline{\frak{Hence : }}}}}$

• $\red\bigstar$ The Amount is Rs.18975.
• $\red\bigstar$ The Compound Interest is Rs.3975.

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

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{red}{Learn More:}}}}}}}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \dag \: \underline{\bf{More \: Useful \: Formula}}\\ {\boxed{\begin{array}{cc}\dashrightarrow {\sf{Amount = Principle + Interest}} \\ \\ \dashrightarrow \sf{ P=Amount - Interest }\\ \\ \dashrightarrow \sf{ S.I = \dfrac{P \times R \times T}{100}} \\ \\ \dashrightarrow \sf{P = \dfrac{Interest \times 100 }{Time \times Rate}} \\ \\ \dashrightarrow \sf{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}} \\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Answer:

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