Question

what is the interest on Rs. 100, at 9 p.c.p.a for 1 year (step by step)​

Answer 1

Answer :-

• The compound interest is Rs 9.

Given :-

• Principal = Rs 100.
• Rate = 9% compounded per annum.
• Time = 1 year.

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 the compound interest. Let's do this step by step!

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For finding the compound interest, we first have to find the amount.

We know that :-

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

Here,

• Principal = Rs 100.
• Rate = 9% compounded per annum.
• Time = 1 year.

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

$\rm Amount = 100\Bigg(1 + \dfrac{9}{100} \Bigg)^{1}$

Making 1 a fraction by taking 1 as the denominator,

$\rm Amount = 100\Bigg( \dfrac{1}{1} + \dfrac{9}{100} \Bigg)^{1}$

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

$\rm Amount = 100\Bigg( \dfrac{1 \times 100 + 9 \times 1}{100} \Bigg)^{1}$

On simplifying,

$\rm Amount = 100\Bigg( \dfrac{100 + 9}{100} \Bigg)^{1}$

Adding 9 to 100,

$\rm Amount = 100\Bigg( \dfrac{109}{100}\Bigg) ^{1}$

The power here is 1, so it won't have any effect on our answer. We will simply remove the brackets.

$\rm Amount = 1 \!\!\!\not0\!\!\! \not0 \times \dfrac{109}{1\!\!\! \not0 \!\!\!\not0}$

Cutting off the zeroes,

$\rm Amount = 1 \times \dfrac{109}{1}$

Now let's multiply the remaining numbers, since we can't reduce them anymore.

$\rm Amount = 1 \times 109$

Multiplying 1 with 109,

$\overline{ \boxed{\rm Amount = Rs \: 109}}$

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We have the amount now, so let's find the compound interest!

We know that :-

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

Here,

• Amount = Rs 109.
• Principal = Rs 100.

Hence,

$\bf CI = 109 - 100$

$\overline{ \boxed{ \bf CI = Rs \: 9}}$

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• So, the compound interest is Rs 9.