Question

Find the difference between the simple interest and the compound interest on ₹20000 at 10% p.a. compounded annually for 3 years.

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Answer 1

Answer:

Difference is ₹620.

Step-by-step explanation:

Given :-

Principal is ₹20000.

Rate of interest is 10%.

Time period is 3 years.

To find :-

Difference between the simple interest and compound interest.

Solution :-

For difference first we will find simple interest and compound interest.

So,

We know,

$\boxed{\bold{Simple \: interest = \dfrac{P \times r \times t}{100}}} </p><p>$

Where,

p is principal, r is rate and t is time, period

$\begin{gathered} \sf \longrightarrow Simple \: interest = \dfrac{20000 \times 10 \times 3}{100} \\ \\ \end{gathered} </p><p>$

$\begin{gathered} \sf \longrightarrow Simple \: interest = \dfrac{600000}{100} \\ \\ \end{gathered} </p><p>$

$\longrightarrow \purple{\boxed{\sf \bold{Simple \: interest = 6000}}\star}$

Thus,

Simple interest is ₹6000.

Interest is compounded annually.

So,

Compound interest = Amount - Principal

Or,

$\boxed{\bold{Compound \: interest = \Bigg\{ P \bigg( 1 + \dfrac{r}{100} \bigg) ^{n} \Bigg\} - P}}$

Put the values :

$\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg(1 + \dfrac{10}{100} \bigg) ^{3} \Bigg\} - 20000 \\ \\ \end{gathered}$

$\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg( \dfrac{100 + 10}{100} \bigg) ^{3} \Bigg\} - 20000 \\ \\ \end{gathered}$

$\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times \bigg(\dfrac{110}{100} \bigg)^{3} \Bigg\} - 20000 \\ \\ \end{gathered}$

$\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{20000 \times \dfrac{1331000}{1000000} \Bigg\} - 20000 \\ \\ \end{gathered}$

$\begin{gathered} \sf \longrightarrow Compound \: interest = \Bigg\{ 20000 \times 1.331 \Bigg\} - 20000 \\ \\ \end{gathered}$

$\begin{gathered} \sf \longrightarrow Compound \: interest = 26620 - 20000 \\ \\ \end{gathered}$

$\begin{gathered} \longrightarrow \red{\boxed{\sf \bold{Compound \: interest = 6620}}\star} \\ \\ \end{gathered}$

Thus,

Compound interest is ₹6620

Now,

Difference = Compound interest - Simple interest

$\sf \longrightarrow 6620 - 6000$

$\sf \longrightarrow \bold{620}$

Therefore,

Difference is ₹620.

Answer 2

Answer:

₹620

Step-by-step explanation:

Answer: Difference is ₹620.