Question

Find the compound interest on a sum of 12,000 at the rate of 8% per annum for 1 year compounded quarter 5. ​

Answer 1

Given :

• Principal = Rs.12000
• Rate = 8 %
• Time = 1 year
• Compound = Quarterly

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To Find :

• Compound Interest = ?

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Solution :

$\dag \; {\underline{\pmb{\frak{ Formula \; Used \; :- }}}}$

• ${\underline{\boxed{\pink{\sf{ A = P \bigg\lgroup 1 + \dfrac{R}{400} \bigg\rgroup ^{4n} }}}}}$

• ${\underline{\boxed{\pink{\sf{ C.I = Amount - Principal }}}}}$

Where :

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

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$\dag \; {\underline{\pmb{\frak{ Calculating \; the \; Amount \; :- }}}}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = P \bigg\lgroup 1 + \dfrac{R}{400} \bigg\rgroup ^{4n} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \bigg\lgroup 1 + \dfrac{8}{400} \bigg\rgroup ^{4 \times 1} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \bigg\lgroup 1 + \dfrac{8}{400} \bigg\rgroup ^{4} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \bigg\lgroup 1 + \cancel\dfrac{8}{400} \bigg\rgroup ^{4} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \bigg\lgroup 1 + \cancel\dfrac{4}{200} \bigg\rgroup ^{4} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \bigg\lgroup 1 + \cancel\dfrac{2}{100} \bigg\rgroup ^{4} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \bigg\lgroup 1 + 0.02 \bigg\rgroup ^{4} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \bigg\lgroup 1.02 \bigg\rgroup ^{4} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \times 1.02 \times 1.02 \times 1.02 \times 1.02 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \times 1.08243216 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; {\qquad{\green{\sf { Amount = ₹ \; 12989.18 }}}} \\ \end{gathered}$

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$\dag \; {\underline{\pmb{\frak{ Calculating \; the \; Compound \; Interest \; :- }}}}$

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

$\begin{gathered} \; \implies \; \; \sf { Compound \; Interest = 12989.18 - 12000 } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; {\qquad{\red{\sf { Compound \; Interest = ₹ \; 989.18 }}}} \\ \end{gathered}$

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$\dag \; {\underline{\pmb{\frak{ Therefore \; :- }}}}$

❛❛ Compound Interest on this sum of money is ₹ 989.18 . ❜❜

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Answer 2

Refer the given attachment