Question

$\mathbb \red{QUESTION : }$
Find the compound interest on Rs.64000 for per 1 year at the rate of 10% p.a. compounded quarterly.
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☆Best Answer::
☆Good explanation::​

Answer 1

$\large{\underline{\underline{\maltese{\red{\pmb{\sf{ \; Given \; :- }}}}}}}$

• Principal = ₹ 64000
• Rate = 10 %
• Time = 1 year
• Compound = Quarterly

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$\large{\underline{\underline{\maltese{\color{maroon}{\pmb{\sf{ \; To \; Find \; :- }}}}}}}$

• Compound Interest = ?

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$\large{\underline{\underline{\maltese{\green{\pmb{\sf{ \; Solution \; :- }}}}}}}$

~ Formula Used :

• Amount :

${\color{cyan}{\bigstar}} \; {\underline{\boxed{\red{\sf{ A = P \bigg[ 1 + \dfrac{R}{400} \bigg]^{4n} }}}}}$

• Compound Interest :

${\color{cyan}{\bigstar}} \; {\underline{\boxed{\red{\sf{ C.I = Amount - Principal }}}}}$

Where :

• A = Amount
• P = Principal
• R = Rate
• n = Time
• C.I = Compound Interest

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~ Calculating the Amount :

$\begin{gathered} \dashrightarrow \qquad{\sf { A = P \bigg[ 1 + \dfrac{R}{400} \bigg]^{4n} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \bigg[ 1 + \dfrac{10}{400} \bigg]^{4 \times 1} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \bigg[ 1 + \dfrac{10}{400} \bigg]^{4} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \bigg[ 1 + \cancel\dfrac{10}{400} \bigg]^{4} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \bigg[ 1 + \cancel\dfrac{5}{200} \bigg]^{4} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \bigg[ 1 + \cancel\dfrac{2.5}{100} \bigg]^{4} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \bigg[ 1 + 0.025 \bigg]^{4} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \bigg[ 1.025 \bigg]^{4} }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \times 1.025 \times 1.025 \times 1.025 \times 1.025 }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \qquad{\sf { A = 64000 \times 1.103812890625 }} \\ \end{gathered}$

$\begin{gathered} \dashrightarrow {\qquad{\orange{\sf { Amount = ₹ \; 70644.025 }}}} \end{gathered}$

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~ Calculating the Compound Interest :

$\begin{gathered} :\implies \qquad{\sf { Compound \; Interest = Amount - Principal }} \\ \end{gathered}$

$\begin{gathered} :\implies \qquad{\sf { Compound \; Interest = 70644.025 - 64000 }} \\ \end{gathered}$

$\begin{gathered} :\implies {\qquad{\purple{\sf { Compound \; Interest = ₹ \; 6644.025 }}}} \end{gathered}$

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~ Therefore :

❝ Compound Interest on this sum of money is ₹ 6644.025 . ❞

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Answer 2

$\purple{ \bigstar} \: \bf\pink{\underline{\underline{Question:}}}$

Find the compound interest on Rs.64000 for per 1 year at the rate of 10% p.a. compounded quarterly.

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$\purple{ \bigstar} \: \bf\blue{\underline{\underline{Given:}}}$

• Principal = ₹64000
• Rate = 10%
• Time = 1 year per annum

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$\purple{ \bigstar} \: \bf\green{\underline{\underline{To \: Find:}}}$

• Compound interest on ₹64000 = ?

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$\purple{ \bigstar} \: \bf\red{\underline{\underline{Solution:}}}$

$\sf\pink{❒ } \: \underline{ \bold{Concept } \: Used :}$

• If P is the Principal then the amount after T years at R% ( rate of compound interest) and n yearly terms will be $\sf{P × (1 + \frac{r}{100n} ) {}^{tn} }$

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$\sf\green{❒ } \: \underline{ Calculating \: the \: \bold{interest} \: compounded \: quarterly \: in \: 3 \: months :}$

$\: \: \: \: \: \: \: \: ⟼ \: \: \: \: \sf{ n = \cancel \frac{12 }{3} }$

$\: \: \: \: \: \: \: \: \: \: \: \sf {⟼ \: \: \: \: \: n = 4 }$

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$\sf\blue{❒} \: \underline{ Finding \: the \: \bold{ Amount } :}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{{ ⟼ \: \: \: \: \: \: \: 64000 \times [{\frac{1 + 10}{(100 \times 4)}] {}^{1 \times 4} } }{ \: }}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: 64000 \times ( \frac{41}{40} ) {}^{4} }{ \: }}$

$\sf{{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ⟼ \: \: \: \: \: \: \: ₹70644.025≈ \green{₹70644} }{ \: }}$

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$\sf\red{❒} \: \underline{Calculating \: the \: \bold{Compound \: Interest } :}$

$\: \:\sf\orange{\underbrace{Compound \: interest = Amount - Principal}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{➺} \: \: \: \: \: \sf{₹(70644 - 64000)}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{➺} \: \: \: \: \: \: \: \sf \pink{₹6644}$

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$\sf\orange{❒} \: \: \underline{Final \: \bold{Answer }:}$

❛ The required compound interest is ₹6644. ❜

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