Question

find simple interest and compound interest both on rupees 30000 at 8 p.c.p.a for 2 years​

Answer 1

Answer :-

• The simple interest is Rs 4800.
• The compound interest is Rs 4992.

Step-by-step explanation :-

• In this question, the principal, rate and time have been given to us. We have to find the simple interest and compound interest.

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Let's find the simple interest first!

We know that :-

$\underline{ \boxed{ \sf SI = \dfrac{Principal \times Rate \times Time}{100}}}$

Here,

• Principal = Rs 30000.
• Rate = 8 p.c.p.a.
• Time = 2 years.

Hence,

$\tt SI = \dfrac{30000 \times 8 \times 2}{100}$

Cutting off the zeroes,

$\tt SI = \dfrac{300 \times 8 \times 2}{1}$

Now let's multiply the remaining numbers.

$\tt SI = 300 \times 8 \times 2$

Multiplying the remaining numbers,

$\overline{\boxed{\tt SI = Rs \: 4800}}$

• The simple interest is Rs 4800.

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Now let's find the compound interest!

First let's find the amount.

We know that :-

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

Here,

• Principal = Rs 30000.
• Rate = 8 p.c.p.a.
• Time = 2 years.

Hence,

$\rm Amount = 30000 \bigg(1 + \dfrac{8}{100} \bigg)^{2}$

Making 1 a fraction by taking 1 as the denominator,

$\rm Amount = 30000 \bigg( \dfrac{1}{1} + \dfrac{8}{100} \bigg)^{2}$

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

$\rm Amount = 30000 \bigg( \dfrac{1 \times 100 + 8 \times 1}{100 } \bigg)^{2}$

On simplifying,

$\rm Amount = 30000 \bigg( \dfrac{100 + 8}{100} \bigg)^{2}$

Adding 8 to 100,

$\rm Amount = 30000 \bigg( \dfrac{108}{100} \bigg) ^{2}$

The power here is 2, so removing the brackets and multiplying 108/100 with itself 2 times,

$\rm Amount = 30000 \times \dfrac{108}{100} \times \dfrac{108}{100}$

Let's multiply 108/100 with itself 2 times first.

$\rm Amount = 30000 \times \dfrac{108 \times 108}{100 \times 100}$

On multiplying,

$\rm Amount = 30000 \times \dfrac{11664}{10000}$

Cutting off the zeroes,

$\rm Amount = 3 \times \dfrac{11664}{1}$

Now let's multiply the remaining numbers.

$\rm Amount = 3 \times 11664$

Multiplying 3 with 11664,

$\overline{\boxed{ \rm Amount = Rs \: 34992}}$

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Now, as we know the amount, let's find the compound interest!

We know that :-

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

Here,

• Amount = Rs 34992.
• Principal = Rs 30000.

Hence,

$\boxed{ \bf CI = 34992 - 30000}$

Subtracting 30000 from 34992,

$\overline{\boxed{ \bf CI = Rs \: 4992}}$

• The compound interest is Rs 4992.

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Abbreviations used :-

$\sf SI = Simple \: Interest.$

$\sf CI = Compound \: Interest.$