Question

Find the amount and CI on Rs. 16000 for year at 15% P.A compounded annually​

Answer 1

Amount = Rs. 18,400

Compound Interest = Rs. 2400.

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Step-by-step explanation:

Principal = Rs. 16,000

Time = 1year

Rate = 15%

Amount = ?

Compound Interest ?

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Calculating Amount

$\sf\large{A = P\bigg(1 + \dfrac{R}{100}\bigg)^n}$

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Putting values in the formula

$\sf\large{=16000 \bigg(1+\dfrac{15}{100} \bigg)^{1} }$

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First calculating under bracket using BODMAS rule.

Making 1 as fraction in the bracket

$\sf\large{= 16000 \bigg(\dfrac{1}{1} + \dfrac{15}{100} \bigg)^{1} }$

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Taking out LCM of 1 and 100 which is 100.

Now multiplying denominator i.e. 1 by 100 and numerator i.e. 1 by 100

$\sf\large{= 16000 \bigg(\dfrac{1 \times 100}{1 \times 100} + \dfrac{15}{100} \bigg)^{1} }$

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After multiplying we can write it as

$\sf\large{= 16000 \bigg(\dfrac{100}{100} + \dfrac{15}{100} \bigg)^{1} }$

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Now denominators are equal, let's add both fractions

$\sf\large{= 16000 \bigg(\dfrac{100 + 5}{100} \bigg)^{1} }$

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On adding 100 and 5 we get 115.

Now cancelling for bringing fraction into simplest form.

$\sf\large{= 16000 \bigg( \cancel\dfrac{115}{100} \bigg)^{1} }$

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After cancellation we can write it as

$\sf\large{ = 16000 \bigg( \dfrac{23}{20} \bigg)^{1} }$

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Multiplying 16000 from fraction 23/20

$\sf\large{ = 16000 \times \dfrac{23}{20} }$

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Cancelling 20 and 16000 to get 800

$\sf\large{ = 800 \times 23}$

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Multiplying to get Amount

$\sf\underline{\large{ = Rs.18,400.}} \:$

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Calculating Compound Interest(C.I.)

C.I. = Final Amount - Original Principal

C.I. = Rs. 18400 - Rs.16000

Compound Interest = Rs. 2400.

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Therefore,

• Amount = Rs. 18400.
• Compound Interest = Rs. 2400.

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Additional Information

Formula for Amount when Interest Compounded:

• Annually = $\sf{A = P\bigg(1 + \dfrac{R}{100}\bigg)^n}$

• Half - yearly = $\sf{A = P\bigg(1 + \dfrac{R}{200}\bigg)^{2n}}$

• Quarterly = $\sf{A = P\bigg(1 + \dfrac{R}{400}\bigg)^{4n}}$.

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