Question

Hey!

Solve the questions :

Find amount and the compound interest :

When ,

1) Principal = ₹5000
Rate = 8% p.a
Number of years = 3 years

Find amount and the compound interest :

When ,

2) Principal = ₹ 4000
Rate = 7.5% p.a
Number of years = 2 years .


​

Answer 1

(1) Answer :-

• Amount = 6298.56 rupees.
• Compound interest = 1298.56 rupees.

Given :-

• Principal = ₹5000
• Rate = 8% p.a
• Time = 3 years

To find :-

• Amount and compound interest.

Step by step explanation :-

Detailed explanation of solution :-

let's understand!

In the question, Given that, Principal, Rate and Time are 5000,8% and 3 years.

We are asked to find amount and compound interest.

How to solve ?

We will find amount first, To find amount, We will use the formula of amount. And then we can easily find compound interest.

Let's do it !

Calculations :-

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

Here, n = Time.

Applying this,

$\implies \sf 5000 \times { \bigg(1 + \dfrac{8}{100} \bigg)}^{3}$

Dividing 8 by 100,

$\implies \sf 5000 \times { \bigg(1 + 0.08 \bigg)}^{3}$

Adding 1 to 0.08,

$\implies \sf 5000 \times { \bigg(1.08 \bigg)}^{3}$

Squaring 1.08, We are left with :-

$\implies \sf 5000 \times 1.259712$

Multiplying 5000 with 1.259712,

$\implies \sf \purple{6298.56}$

Thus, Amount = 6298.56 Rupees.

For compound interest :-

$\boxed{ \mathfrak{Compound \: interest = Amount - Principal}}$

Applying this,

$\implies \sf 6298.56 - 5000$

Subtracting 5000 from 6298.56,

$\implies \sf \purple{ 1298.56 }$

Therefore, Compound interest = 1298.56 rupees.

$\rule{300}{1}$

(2) Answer :-

Amount = 4622.5 rupees.

Compound interest = 622.5 rupees.

Given :-

Principal = ₹ 4000

Rate = 7.5% p.a

Time = 2 years

To find :-

Amount and compound interest.

Step by step explanation :-

Detailed explanation of solution :-

let's understand!

In the question, Given that, Principal, Rate and Time are ₹ 4000 , 7.5% p.a and 2 years.

We are asked to find amount and compound interest.

How to solve ?

We will find amount first, To find amount, We will use the formula of amount. And then we can easily find compound interest.

Let's do it !

Calculations :-

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

Here, n = Time.

Applying this,

$\implies \sf 4000{ \bigg(1 + \dfrac{7.5}{100} \bigg)}^{2}$

Dividing 7.5 by 100,

$\implies \sf 4000{ \bigg(1 + 0.075 \bigg)}^{2}$

Adding 1 to 0.075,

$\implies \sf 4000{ \bigg(1.075 \bigg)}^{2}$

Squaring 1.075, We are left with :-

$\implies \sf 4000 \times 1.155625$

Multiplying 4000 with 1.155625,

$\implies \sf \purple{4622.5}$

Thus, Amount = 4622.5 rupees.

For compound interest :-

$\boxed{ \mathfrak{Compound \: interest = Amount - Principal}}$

Applying this,

$\implies \sf 4622.5 - 4000$

Subtracting 4000 from 4622.5

$\implies \sf \purple{622.5}$

Therefore, Compound interest = 622.5 rupees.

Answer 2

$\Large{\underbrace{\underline{\sf{Understanding\; the\; Concept}}}}$

Here in this question, concept of compounding of interest is used. We are asked to find amount and compound interest for certain years at a given rate on the given principal amount. We have particular formula for calculation of amount and compound interest. Before finding it, let's understanding what compound interest actually is!

Compound interest→ The interest which is calculated on the basis of principal and interest is called compound interest. It can also be said as “Intrest on Intrest”. It is much profitable than simple interest.

So let's start solving!!

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Solution 1

Given:

• Principal, P=Rs. 5000

• Rate, R=8% per annum (p.a.)

• Number of years, n=3 years

_____________________________

To find:

• Amount

• Compound Interest

_____________________________

Solution:

We have formula for amount:

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

Now substitute the given values!

$\sf {\Longrightarrow A=5000\bigg(1+\dfrac{8}{100}\bigg)^3}$

Now solve the fraction!

$\sf {\Longrightarrow A=5000\bigg(1+0.08}\bigg)^3}$

$\sf\bigg[\because\dfrac{8}{100}=0.08\bigg]$

$\sf {\Longrightarrow A=5000\bigg(1.08}\bigg)^3}$

$\sf\big[1+0.08=1.08\big]$

Now solve the cube of 1.08!

$\sf {\Longrightarrow A=5000\times 1.259712$

Now multiply it!

$\underline{\boxed{ {\sf{\green{A}}}{\green{=}}{\mathfrak{\green{6298.56}}}}}$

So the amount is Rs.6298.56

$\rule{290}{2}$

Now apply formula for compound interest:

$\underline{\boxed{\sf Compound\: Interest=Amount-Principal}}\bigstar$

$\sf Compound \:interest=Rs.6298.56- Rs.5000$

${\boxed{\sf {\blue{Compound \:interest=Rs.1298.56}}}}$

So the value of compound interest is Rs. 1298.56

$\rule{290}{2}$

Solution 2

Given:

• Principal, P=Rs.4000

• Rate, R=7.5 % per annum (p.a.)

• Number of years, n=2 years

_____________________________

To find:

• Amount

• Compound Interest

_____________________________

Solution:

Formula for Amount:-

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

Now substitute given values!

$\sf {\Longrightarrow A=4000\bigg(1+\dfrac{7.5}{100}\bigg)^2}$

Now solve the fraction!

$\sf {\Longrightarrow A=4000\bigg(1+0.075\bigg)^2}$

$\sf \bigg[\because \dfrac{7.5}{100}=0.075\bigg]$

Now add it!

$\sf {\Longrightarrow A=4000\bigg(1.075\bigg)^2}$

$\sf\big[\because 1+0.075=1.075\big]$

Now squaring of 1.075!

$\sf {\Longrightarrow A=4000\times 1.155625$

Now multiply it!

$\underline{\boxed{{\sf \red{A}}\red{=}\mathfrak{\red{4622.5}}}}$

So the amount is Rs. 4622.5.

$\rule{290}{2}$

Now applying formula for compound interest:

$\underline{\boxed{\sf Compound\: Interest=Amount-Principal}}\bigstar$

$\sf Compound\: Interest=Rs.4622.5-Rs.4000$

${\boxed{\sf {\pink{Compound\; Interest=Rs. 622.5}}}}$

So the compound interest is Rs. 622.5

$\rule{290}{2}$

Required Answer:-

Solution 1:

• Compound Interest=Rs. 1298.56

• Amount= Rs. 6298.56

Solution 2:

• Compound Interest= Rs. 622.5

• Amount= Rs. 4622.5

$\rule{290}{2}$

Additional information:-

Formula of simple interest:

$\underline{\boxed{\sf S.I=\dfrac{P\times R \times T}{100}}}\bigstar$

Here:-

• P refers to “Principal”

• R refers to “Rate of Interest”

• T refers to “ Time for which money is deposited ”.

$\rule{290}{2}$

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