Question

please answer to my question
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Answer 1

Answer:

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Given :}}}}}}}\end{gathered}$

• ↠ Principle = ₹6400
• ↠ Time = 2 years
• ↠ Rate of Interest = 15½%

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

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:To Find :}}}}}}}\end{gathered}$

• ↠ Compound Interest

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

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Concept :}}}}}}}\end{gathered}$

⊙ Here we have given that the Principal is ₹6400, Time is 2 years and rate is 11/2 p.c.p.a. As we know that to find the compound interest we need Amount. So firstly we will find out the amount.

⊙ After finding the amount we will find out the Compound Interest by substituting the values in the formula.

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

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Using Formulae :}}}}}}}\end{gathered}$

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

$\quad\bigstar{\underline{\boxed{\sf{C.I= A - P }}}}$

$\purple\bigstar$ Where

• ★ P = Principle
• ★ R = Rate of Interest
• ★ T = Time
• ★ A = Amount
• ★ C.I = Compound Interest

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

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Solution :}}}}}}}\end{gathered}$

$\purple\bigstar$ Here :-

• Principle = ₹6400
• Time = 2 years
• Rate of Interest = 11/2%

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

$\purple\bigstar$ Firstly, Finding the Amount :-

$\quad{\small{\dashrightarrow{\tt{A ={P{\bigg(1 + \dfrac{R}{100}{\bigg)}^{T}}}}}}}$

• Substituting the values

$\quad{\small{\dashrightarrow{\tt{A ={6400{\bigg(1 + \dfrac{11}{2 \times 100}{\bigg)}^{2}}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={6400{\bigg(1 + \dfrac{11}{200}{\bigg)}^{2}}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={6400{\bigg(\dfrac{(1 \times200) + (11 \times 1)}{200}{\bigg)}^{2}}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={6400{\bigg(\dfrac{200 + 11}{200}{\bigg)}^{2}}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={6400{\bigg(\dfrac{211}{200}{\bigg)}^{2}}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={6400{\bigg(\dfrac{211}{200} \times \dfrac{211}{200}{\bigg)}}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={6400{\bigg(\dfrac{44521}{40000}{\bigg)}}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={6400 \times \dfrac{44521}{40000}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={\dfrac{6400 \times 44521}{40000}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={\dfrac{284934400}{40000}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={ \cancel\dfrac{284934400}{40000}}}}}}$

$\quad{\small{\dashrightarrow{\tt{A ={7123.36}}}}}$

$\quad\bigstar{\underline{\boxed{\pmb{\sf{\red{ Amount={7123.36}}}}}}}$

∴ The Amount is ₹7123.36.

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

$\purple\bigstar$ Now, Calculating the Compound Interest :-

$\quad{\dashrightarrow{\tt{C.I= A - P }}}$

• Substuting the values

$\quad{\dashrightarrow{\tt{C.I= 7123.36- 6400 }}}$

$\quad{\dashrightarrow{\tt{C.I= 723.36}}}$

$\quad\bigstar{\underline{\boxed{\pmb{\sf{\red{Compound \: Interest = 723.36}}}}}}$

∴ The Compound Interest is ₹723.36.

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

$\begin{gathered}{\large{\underline{\underline{\maltese{\textsf{\textbf{\:Learn More :}}}}}}}\end{gathered}$

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

$\quad{\longrightarrow{\sf{Amount = Principle + Interest}}}$

$\quad{\longrightarrow{\sf{ P=Amount - Interest }}}$

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

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

$\quad{\longrightarrow{\sf{P = \dfrac{Interest \times 100 }{Time \times Rate}}}}$

$\quad{\longrightarrow{\sf{Rate = \dfrac{Simple \: Interest \times 100}{Principle \times Time}}}}$

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