Math, asked by faizalkhan6371, 7 months ago

find the distance between the simple interest and the compound interest and the compound interest on Rs 5000 for 2 years at 6% per annum

Answers

Answered by Anonymous
29

» Question :

Find the distance between the Simple Interest and the Compound Interest on ₹ 5000 for 2 years at 6% per annum.

» To Find :

The difference between the Simple Interest and the Compound Interest.

» Given :

  • Principal = ₹ 5000

  • Time = 3 years

  • Rate = 6% p.a.

» We Know :

Formula for Simple Interest :

\bf{\underline{\boxed{SI = \dfrac{P \times R \times t}{100}}}}

Where,

  • P = Principal
  • R = Rate
  • t = Time
  • SI = Simple Interest

Formula for Compound Interest :

\bf{\underline{\boxed{CI = Amount - Principal}}}

Formula for Amount :

\bf{\underline{\boxed{A = P\bigg(1 + \dfrac{R}{100}\bigg)^{n}}}}

Where,

  • P = Principal
  • A = Amount
  • R = Rate
  • n = time period

» Concept :

To Find the difference between the Simple Interest and the Compound Interest , first we have to find the Individual simple and compound interest .

And then by subtracting them with each other ,we can find the difference between them.

» Solution :

Simple Interest :

We Know,

  • Principal = ₹ 5000

  • Time = 3 years

  • Rate = 6% p.a.

Formula :

\sf{SI = \dfrac{P \times R \times t}{100}}

Putting the value in the formula , we get :

\sf{\Rightarrow SI = \dfrac{5000 \times 6 \times 2}{100}}

\sf{\Rightarrow SI = \dfrac{50\cancel{00} \times 6 \times 2}{\cancel{100}}}

\sf{\Rightarrow SI = 50 \times 6 \times 2}

\sf{\Rightarrow SI = 600}

Hence, the simple interest is ₹ 600.

Compound interest :

Amount :

We Know :

  • Principal = ₹ 5000
  • Time = 3 years
  • Rate = 6% p.a.

Formula :

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

Putting the value in the formula , we get :

\sf{\Rightarrow A = 5000\bigg(1 + \dfrac{6}{100}\bigg)^{2}}

\sf{\Rightarrow A = 5000\bigg(\dfrac{100 + 6}{100}\bigg)^{2}}

\sf{\Rightarrow A = 5000\bigg(\dfrac{106}{100}\bigg)^{2}}

\sf{\Rightarrow A = 5000 \times \dfrac{106}{100} \times \dfrac{106}{100}}

\sf{\Rightarrow A = 5\cancel{000} \times \dfrac{106}{\cancel{100}} \times \dfrac{106}{10\cancel{0}}}

\sf{\Rightarrow A = 5 \times 106 \times \dfrac{106}{10}}

\sf{\Rightarrow A = \dfrac{56180}{10}}

\sf{\Rightarrow A = \dfrac{5618\cancel{0}}{\cancel{10}}}

\sf{\Rightarrow A = 5618}

Hence ,the amount is ₹5618.

Compound interest :

Formula :

\sf{CI = Amount - Principal}

Putting the value in the formula ,we get :

\sf{\Rightarrow CI = 5618 - 5000}

\sf{\Rightarrow CI = 618}

Hence the CI is ₹618.

Difference between the Simple Interest and the Compound Interest:

  • Simple Interest = ₹600
  • Compound Interest = ₹618

Difference = Compound Interest - Simple Interest

\sf{\Rightarrow 618 - 600}

\sf{\Rightarrow 18}

Hence the difference between the Simple Interest and the Compound Interest is ₹18.

Additional information :

  • \sf{P = \dfrac{SI \times 100}{R \times t}}

  • \sf{R = \dfrac{SI \times 100}{P \times t}}

  • \sf{T = \dfrac{SI \times 100}{R \times P}}

  • Amount = Principal + Simple Interest

Where ,

P = Principal

A = Amount

R = Rate

t = time

SI = Simple Interest

Answered by BrainlyHera
12

Given :

  • principal = 5000
  • time period = 2 years
  • rate = 6 % per annum

To Find:

  • simple interest
  • compound interest
  • difference between simple and compound interest

Formula :

 \bigstar \:  \mathtt {SI =  \dfrac{P× R× t }{100}}

\bigstar \:  \mathtt {A =P{(1 +  \dfrac{R}{100} })  ^{n}}

\bigstar \:  \mathtt {CI= A - P}

here ,

  • SI = simple interest
  • P = principal
  • R = rate
  • n= t = time period
  • A = amount
  • CI = compound interest

Solution :

Step 1 : Find simple interest

\bigstar \:  \mathtt {SI =  \dfrac{P× R× t }{100}}

here ,

  • P = Rs 5000
  • R = 6 %
  • t = 2 years

\rightarrow \:  \mathtt {SI =  \dfrac{5000× 6× 2 }{100}}

\rightarrow \:  \mathtt {SI =  \dfrac{600 \cancel{00}}{ \cancel{100}}}

\rightarrow \:  \mathtt {SI =  Rs \:  600}

_______________________________

Step 2 : Find Amount

\bigstar \:  \mathtt {A =P{(1 +  \dfrac{R}{100} })  ^{n}}

here ,

  • P = Rs 5000
  • R = 6 %
  • n = t = 2

\rightarrow \:  \mathtt {A =5000{(1 +  \dfrac{6}{100} })  ^{2}}

\rightarrow \:  \mathtt {A =5000{( \dfrac{106}{100} })  ^{2}}

\rightarrow \:  \mathtt {A =5 \cancel{000}{( \dfrac{11236}{10 \cancel{000}} })  }

\rightarrow \:  \mathtt {A =5 \times 1123.6}

\rightarrow \:  \mathtt {A =Rs 5618}

________________________________

Step 3 : Find the compound interest

\bigstar \:  \mathtt {CI= A - P}

here ,

  • A = Rs 5618
  • P = Rs 5000

\rightarrow\:  \mathtt {CI= 5618 - 5000}

\rightarrow\:  \mathtt {CI=Rs 618}

________________________________

Step 4: Find the difference between compound interest and simple interest

= 618 - 600

= Rs 18

Difference between compound interest and simple interest is Rs 18

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