Question

calculate the difference between the compound interest on ₹ 25,000 for 2 years at rate at 10% per annum when compounded hafly yearly and quarterly​

Answer 1

Solution :

${\red{❒}}$ Formula Used :

• ${\underline{\boxed{\purple{\sf{ Amount{\small_{(Half - yearly) }} = P \bigg( 1 + \dfrac{R}{200} \bigg) ^{2n} }}}}}$

• ${\underline{\boxed{\purple{\sf{ Amount{\small_{(Quarterly) }} = P \bigg( 1 + \dfrac{R}{400} \bigg) ^{4n} }}}}}$

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

Where :

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

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${\red{❒}}$ Calculating the Amount (Half - yearly) :

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

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \dfrac{10}{200} \bigg) ^{2 \times 2} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \dfrac{10}{200} \bigg) ^{4} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \cancel\dfrac{10}{200} \bigg) ^{4} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \cancel\dfrac{5}{100} \bigg) ^{4} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + 0.05 \bigg) ^{4} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + 0.05 \bigg) ^{4} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1.05 \bigg) ^{4} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \times 1.05 \times 1.05 \times 1.05 \times 1.05 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \times 1.21550625 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; {\qquad{\green{\sf { Amount = ₹ \; 30387.65 }}}} \\ \end{gathered}$

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${\red{❒}}$ Calculating the Compound interest :

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

$\begin{gathered} \implies \; \; \sf { Compound \; Interest = 30387.65 - 25000 } \\ \end{gathered}$

$\begin{gathered} \implies \; \; {\qquad{\orange{\sf { Compound \: Interest = ₹ \; 5387.65 }}}} \\ \end{gathered}$

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${\red{❒}}$ Calculating the Amount (Quarterly) :

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

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \dfrac{10}{400} \bigg) ^{4 \times 2} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \dfrac{10}{400} \bigg) ^{8} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \cancel\dfrac{10}{400} \bigg) ^{8} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \cancel\dfrac{5}{200} \bigg) ^{8} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + \cancel\dfrac{2.5}{100} \bigg) ^{8} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1 + 0.025 \bigg) ^{8} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \bigg( 1.025 \bigg) ^{8} } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; \sf { A = 25000 \times 1.21840289751 } \\ \end{gathered}$

$\begin{gathered} \dashrightarrow \; \; {\qquad{\green{\sf { Amount = ₹ \; 30460.07 }}}} \\ \end{gathered}$

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${\red{❒}}$ Calculating the Compound interest :

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

$\begin{gathered} \implies \; \; \sf { Compound \; Interest = 30460.07 - 25000 } \\ \end{gathered}$

$\begin{gathered} \implies \; \; {\qquad{\orange{\sf { Compound \; Interest = ₹ \; 5460.07 }}}} \\ \end{gathered}$

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${\red{❒}}$ Calculating the Difference :

$\begin{gathered} \twoheadrightarrow \; \; \sf { Difference = Interest{\small_{(Quarterly)}} - Interest{\small_{(Half - yearly)}} } \\ \end{gathered}$

$\begin{gathered} \twoheadrightarrow \; \; \sf { Difference = 5460.07 - 5387.65 } \\ \end{gathered}$

$\begin{gathered} \twoheadrightarrow \; \; {\qquad{\pink{\sf { Difference = ₹ \; 72.42 (Approx.) }}}} \\ \end{gathered}$

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${\red{❒}}$ Therefore :

❛❛ Difference between the Compound interest at Half - yearly and Quarterly is ₹ 72.42 (Approx.) . ❜❜

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Answer 2

Answer:

What is the largest source of groundwater in the Indian peninsula?csuuqnttpf