15% of ₹45000 How much compound interest accrued at the end of 2 yea – InterviewSolution

1.

15% of ₹45000 How much compound interest accrued at the end of 2 years at the rate

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ong>Question :-

How much compound interest will be accrued at the end of 2 years at the rate of 15% PER annum for the principal of Rs 45000 compounded annually?

Answer :-

The compound interest accrued at the end of 2 years at the rate of 15% per annum for the principal of Rs 45000 compounded annually is Rs 14512.5

To find :-

The Compound Interest.

Step-by-step explanation :-

In this question, the principal, rate and time has been given to US. We have to find out the compound interest. For this, first we are going to find the amount and then use it to find the compound interest.

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To find the compound interest, let's find the amount first!

We know that :-

$\underline{\boxed{\sf Amount = Principal \Bigg(1+\dfrac{Rate}{100} \Bigg)^{Time}}}$

Here,

Principal = Rs 45000.
Rate = 15% per annum compounded annually.
Time = 2 years.

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$\underline{\underline{\mathfrak{Substituting\: the \:given \:values,}}}$

$\rightarrow\rm Amount = 45000 \Bigg(1 + \dfrac{15}{100} \Bigg)^2$

Taking 1 as the denominator and making 1 a fraction.

$\rightarrow\rm Amount = \Bigg(\dfrac{1}{1} + \dfrac{15}{100} \Bigg)^2$

The LCM of 1 and 100 is 100, therefore on multiplying the fractions using their denominators,

$\rightarrow\rm Amount = 45000 \Bigg(\dfrac{1 \times 100 + 15 \times 1}{100} \Bigg)^2$

On simplifying,

$\rightarrow\rm Amount = 45000 \Bigg(\dfrac{100 + 15}{100} \Bigg)^2$

Adding 15 to 100,

$\rightarrow\rm Amount = 45000 \Bigg(\dfrac{115}{100} \Bigg)^2$

The POWER here is 2, so REMOVING the brackets and multiplying 115/100 by itself 2 times,

$\rightarrow\rm Amount = 45000 \times \dfrac{115}{100} \times \dfrac{115}{100}$

First let's multiply 115/100 with 115/100.

$\rightarrow\rm Amount = 45000 \times \dfrac{115\times115}{100\times100}$

On multiplying the numbers,

$\rightarrow\rm Amount = 45000 \times\dfrac{13225}{10000}$

Cutting off the zeroes,

$\rightarrow\rm Amount = 45 \times \dfrac{13225}{10}$

Reducing the numbers,

$\rightarrow\rm Amount = 9 \times \dfrac{13225}{2}$

Now on multiplying the remaining numbers, we get :-

$\rightarrow\rm Amount = \dfrac{119025}{2}$

Dividing 119025 by 2,

$\rightarrow{\overline{\boxed{\rm Amount = Rs \: 59512.5}}}$

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Now, since we know the amount, therefore let's find out the compound interest!

We know that :-

$\underline{\boxed{\sf CI = Amount - Principal}}$

Here,

Amount = Rs 59512.5
Principal = Rs 45000.

Hence,

$\boxed{\bf C \: I = 59512.5 - 45000}$

Subtracting 45000 from 59512.5,

$\overline{\boxed{\bf C \: I = Rs \:14512.5}}$

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Hence, the compound interest is Rs 14512.5

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$\underline{\bf Abbreviation \: used :-}$

$\sf CI = Compound \: Interest.$

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