Question

Find the compound interest on 12,000 at rate of interest of 12% for one year, if the interest is being compounded half-yearly,​

Answer 1

Given :

• Principal = Rs.12000
• Rate = 12 %
• Time = 1 year
• Compounded = Half - yearly

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To Find :

• Compound Interest = ?

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Solution :

~ Formula Used :

• Amount :

$\large{\color{cyan}{\bigstar}} \; \; {\underline{\boxed{\red{\sf{ A = P\bigg\lgroup 1 + \dfrac{R}{200} \bigg\rgroup^{2n} }}}}}$

• Compound Interest :

$\large{\color{cyan}{\bigstar}} \; \; {\underline{\boxed{\red{\sf{ Compound \; Interest = Amount - Principal }}}}}$

Where :

• $\twoheadrightarrow$ A = Amount
• $\twoheadrightarrow$ R = Rate
• $\twoheadrightarrow$ P = Principal
• $\twoheadrightarrow$ n = Time

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~ Calculating the Amount :

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = P\bigg\lgroup 1 + \dfrac{R}{200} \bigg\rgroup^{2n} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000\bigg\lgroup 1 + \dfrac{12}{200} \bigg\rgroup^{2 \times 1} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000\bigg\lgroup 1 + \dfrac{12}{200} \bigg\rgroup^{2} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000\bigg\lgroup 1 + \cancel\dfrac{12}{200} \bigg\rgroup^{2} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000\bigg\lgroup 1 + \cancel\dfrac{6}{100} \bigg\rgroup^{2} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000\bigg\lgroup 1 + 0.06 \bigg\rgroup^{2} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000\bigg\lgroup 1.06 \bigg\rgroup^{2} } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \times 1.06 \times 1.06 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; \sf { A = 12000 \times 1.1236 } \\ \end{gathered}$

$\begin{gathered} \; \dashrightarrow \; \; {\qquad{\orange{\sf { Amount = ₹ \; 13483.2 }}}} \\ \end{gathered}$

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~ Calculating the Compound Interest :

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

$\begin{gathered} \; \implies \; \; \sf { Compound \; Interest = 13483.2 - 12000 } \\ \end{gathered}$

$\begin{gathered} \; \implies \; \; {\qquad{\purple{\sf { Compound \; Interest = ₹ \; 1483.2 }}}} \\ \end{gathered}$

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~ Therefore :

❛❛ Compound Interest on this sum of money is ₹ 1483.2 . ❜❜

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