Question

A person deposited a certain amount with a leasing company at the rate of interest of 20% compounded annually. At the end of 3 years , he received back Rs 21,600. Find the amount deposited.
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Answer 1

Given :

• Amount = 21600
• Rate = 20 %
• Time = 3 years

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To Find :

• Principal = ?

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Solution :

~ Formula Used :

$\large{\color{darkblue}{\dashrightarrow}} \: \: {\underline{\overline{\boxed{\red{\sf{ A = P \bigg[ 1 + \dfrac{R}{100} \bigg]^T }}}}}}$

Where :

• A = Amount
• P = Principal
• R = Rate
• T = Time

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Principal :

${:\implies{\qquad{\rm{ A = P \bigg[ 1 + \dfrac{R}{100} \bigg]^T }}}} \\ \\ \ {:\implies{\qquad{\rm{ 21600 = P \bigg[ 1 + \dfrac{20}{100} \bigg]^3 }}}} \\ \\ \ {:\implies{\qquad{\rm{ 21600 = P \bigg[ 1 + \cancel\dfrac{20}{100} \bigg]^3 }}}} \\ \\ \ {:\implies{\qquad{\rm{ 21600 = P \bigg[ 1 + 0.20 \bigg]^3 }}}} \\ \\ \ {:\implies{\qquad{\rm{ 21600 = P \bigg[ 1.20 \bigg]^3 }}}} \\ \\ \ {:\implies{\qquad{\rm{ 21600 = P \times 1.20 \times 1.20 \times 1.20 }}}} \\ \\ \ {:\implies{\qquad{\rm{ 21600 = P \times 1.728 }}}} \\ \\ \ {:\implies{\qquad{\rm{ \cancel\dfrac{21600}{1.728} = P }}}} \\ \\ \ {\qquad{\textsf{ Principal of this amount = {\color{maroon}{\sf{ ₹ \: 12500 }}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

Therefore :

❝ Principal of this Amount is ₹ 12500 . ❞

$\\ {\orange{\underline{\rule{75pt}{9pt}}}}{\color{cyan}{\underline{\rule{75pt}{9pt}}}}{\red{\underline{\rule{75pt}{9pt}}}}$

Answer 2

Principal of this Amount (P) = ₹ 12,500