Question

For principal amount Rs. 5000 at the rate of 8 p.c.p.a. for 3 years duration compound interest​

Answer 1

Answer :-

• The compound interest is Rs 1298.56.

Given :-

• Principal = Rs 5000.
• Rate = 8 p.c.p.a.
• Time = 3 years.

To find :-

• The compound interest.

Step-by-step explanation :-

• Let's find the amount first, then we will use it to find the compound interest!

We know that :-

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

Here,

• Principal = Rs 5000.
• Rate = 8 p.c.p.a.
• Time = 3 years.

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Hence,

$\rm Amount = 5000 \bigg(1 + \dfrac{8}{100} \bigg)^{3}$

Making 1 a fraction by taking 1 as the denominator,

$\rm Amount = 5000 \bigg( \dfrac{1}{1} + \dfrac{8}{100} \bigg)^{3}$

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

$\rm Amount = 5000 \bigg( \dfrac{1 \times 100 + 8 \times 1}{100} \bigg)^{3}$

On simplifying,

$\rm Amount = 5000 \bigg( \dfrac{100 + 8}{100} \bigg)^{3}$

Adding 8 to 100,

$\rm Amount =5000 \bigg( \dfrac{108}{100} \bigg)^{3}$

The power here is 3, so removing the brackets and multiplying 108/100 with itself 3 times,

$\rm Amount = 5000 \times \dfrac{108}{100} \times \dfrac{108}{100} \times \dfrac{108}{100}$

Let's multiply 108/100 with itself 3 times first.

$\rm Amount = 5000 \times \dfrac{108 \times 108 \times 108}{100 \times 100 \times 100}$

On multiplying,

$\rm Amount = 5\!\!\!\not0\!\!\!\not0\!\!\!\not0 \times \dfrac{1259712}{1000\!\!\!\not0\!\!\!\not0\!\!\!\not0}$

Cutting off the zeroes,

$\rm Amount = 5 \times \dfrac{1259712}{1000}$

Multiplying 5 with 1259712,

$\rm Amount = \dfrac{6298560}{1000}$

Dividing 6298560 by 1000,

$\overline{\boxed{\rm Amount = Rs \: 6298.56}}$

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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 6298.56.
• Principal = Rs 5000.

Hence,

$\boxed{\bf CI =6298.56 - 5000}$

Subtracting 5000 from 6298.56,

$\overline{ \boxed{ \bf CI = Rs \: 1298.56}}$

• Hence, the compound interest = Rs 1298.56.

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Abbreviations used :-

$\sf CI = Compound \: Interest.$

Answer 2

Given :

• Principal (P) = Rs 5000
• Time (n) = 3 years
• Rate (R) = 8% per annum

To Find :

• Compound interest

Formulas :

$\red \bigstar \: {\underline{\boxed{\mathcal {\pmb{\quad Amount \: = \: Principal \: \times \bigg(\:1 \: + \: \dfrac{Rate}{100}\bigg)^{n}\quad}}}}}$

$\red \bigstar \: {\underline{\boxed{\mathcal {\pmb{\quad Compound \: Interest \: = \: Amount \: - \: Principal \quad}}}}}$

Solution :

${:} \longrightarrow \sf \: Amount \: = \: Principal \: \times \bigg(\:1 \: + \: \dfrac{Rate}{100}\bigg)^{n} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 5000 \: \times \bigg(\:1 \: + \: \dfrac{8}{100}\bigg)^{3} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 5000 \: \times \bigg(\dfrac{108}{100}\bigg)^{3} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 5000\: \times \: \dfrac{108}{100} \: \times \: \dfrac{108}{100} \: \times \: \dfrac{108}{100} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: 5\cancel{000} \: \times \: \dfrac{108}{1 \cancel{00}} \: \times \: \dfrac{108}{10 \cancel{0}} \: \times \: \dfrac{108}{100} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: \dfrac{5 \: \times \: 108 \: \times \: 108 \: \times \: 108}{10 \: \times \: 100} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: \dfrac{540\: \times \: 11,664}{ 1000} \\ \\ {:} \longrightarrow \sf \: Amount \: = \: \dfrac{62,98,560}{ 1000} \\ \\ {:} \longrightarrow \underline{\boxed{\sf \: Amount \: = \: Rs \: 6298.56}} \: \blue \bigstar$

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$\longmapsto {\pmb{ Compound \: Interest \: = \: Amount \: - \: Principal} } \\ \\ \longmapsto {\sf{ Compound \: Interest \: = \: 6298.56 \: - \: 5000} } \\ \\ \longmapsto \underline{\boxed{\pmb{ \red{ Compound \: Interest \: = \:Rs \:1,298.56} }}}$

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$\qquad \therefore\: \sf{ Amount \: = \underline {\underline{ Rs \: 6298.56}}}$

$\qquad \therefore\: \sf{ Compound \: Interest\: = \underline {\underline{ Rs \: 1,298.56}}}$

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