Question

find the amount and the compound interest on rupees 20000 for one 1 by 2 years at the rate of 8% per annum compounded half yearly...​

Answer 1

Answer:

Refer the above attachment..✍

Answer 2

Given :

• Principal = 20000
• Rate = 8 %
• Time = ${\sf{ 1\dfrac{1}{2} }}$ years

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To Find :

• Compound Interest = ?
• Amount = ?

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Solution :

~ Formula Used :

• Amount :

${\color{cyan}{\bigstar}} \; \; {\underline{\overline{\boxed{\red{\sf{ Amount = Principal \bigg[ 1 + \dfrac{Rate}{200} \bigg]^{2 \times Time} }}}}}}$

• Compound Interest :

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

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~ Calculating the Amount :

${\longmapsto{\qquad{\sf{ Amount = Principal \bigg[ 1 + \dfrac{Rate}{200} \bigg]^{2 \times Time} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1 + \dfrac{8}{100} \bigg]^{2 \times 1\frac{1}{2} } }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1 + \dfrac{8}{200} \bigg]^{2 \times \dfrac{3}{2} } }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1 + \dfrac{8}{200} \bigg]^{ \dfrac{6}{2} } }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1 + \dfrac{8}{200} \bigg]^{ \cancel\frac{6}{2} } }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1 + \dfrac{8}{200} \bigg]^{3} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1 + \cancel\dfrac{8}{200} \bigg]^{3} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1 + \cancel\dfrac{4}{100} \bigg]^{3} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1 + 0.04 \bigg]^{3} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \bigg[ 1.04 \bigg]^{3} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \times 1.04 \times 1.04 \times 1.04 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Amount = 20000 \times 1.124864 }}}} \\ \\ \ {\qquad \; \; \; {\therefore \; {\underline{\boxed{\green{\sf{Amount = ₹ \; 22497.28 }}}}}}}$

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~ Calculating the Compound Interest :

${\dashrightarrow{\qquad{\sf{ Compound\; Interest = Amount - Principal }}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Compound\; Interest = 22497.28 - 20000 }}}} \\ \\ \ {\qquad \; \; \; {\therefore \; {\underline{\boxed{\orange{\sf{Compound \; Interest = ₹ \; 2497.28 }}}}}}}$

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~ Therefore :

❛❛ Amount is ₹ 22497.28 and the Compound Interest is ₹ 2497.28 . ❜❜

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