Question

Find the amount and the compound interest when principal is Rs. 2000 ,rate is 8 %per annum and time is 1 year . The interest is being payable quarterly.​

Answer 1

The amount that is getting is as follows-

Rs. 2000 x 1.331 = Rs. 2662

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Answer 2

$\star \; {\underline{\boxed{\pmb{\red{\frak{ \; Given \; :- }}}}}}$

• Principal = Rs.2000
• Rate = 8 %
• Time = 1 year
• Compounded = Quarterly

$\star \; {\underline{\boxed{\pmb{\orange{\frak{ \; To \; Find \; :- }}}}}}$

• Amount = ?
• Compound Interest = ?

$\star \; {\underline{\boxed{\pmb{\green{\frak{ \; SolutioN \; :- }}}}}}$

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ A = P \bigg[ 1 + \dfrac{R}{400} \bigg]^{4n} }}}}}$

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

Where :

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

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$\maltese$ Calculating the Amount :

${\dashrightarrow{\qquad{\sf{ A = P \bigg[ 1 + \dfrac{R}{400} \bigg]^{4n} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \bigg[ 1 + \dfrac{8}{400} \bigg]^{4 \times 1} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \bigg[ 1 + \dfrac{8}{400} \bigg]^4 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \bigg[ 1 + \cancel\dfrac{8}{400} \bigg]^4 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \bigg[ 1 + \cancel\dfrac{4}{200} \bigg]^4 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \bigg[ 1 + \cancel\dfrac{2}{100} \bigg]^4 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \bigg[ 1 + 0.02 \bigg]^4 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \bigg[ 1.02 \bigg]^4 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \times 1.02 \times 1.02 \times 1.02 \times 1.02 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ A = 2000 \times 1.08243216 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\pink{\sf{ Amount = ₹ \; 2164.86 \; \bigg\lgroup Approx. \bigg\rgroup }}}}}}}}$

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$\maltese$ Calculating the Compound Interest :

${\longmapsto{\qquad{\sf{ Compound \; Interst = Amount - Principal }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Compound \; Interest = 2146.86 - 2000 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\purple{\sf{ Compound \; Interest = ₹ \; 164.86 \; \bigg\lgroup Approx. \bigg\rgroup }}}}}}}}$

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$\maltese$ Therefore :

❛❛ Amount on this sum of money is ₹ 2164.86 and Compound Interest is ₹ 164.86 . ❜❜

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