Question

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

Answer 1

» 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

Answer 2

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