Question

Find the difference between the simple interest and compound interest on ₹20,000 . at 10% p.a compound anullay for 3 years​

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,

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

Where,

• P is principal, r is rate of interest and t is time period.

Put all values :

$\sf \longrightarrow Simple \: interest = \dfrac{20000 \times 10 \times 3}{100}$

$\sf \longrightarrow Simple \: interest = \dfrac{600000}{100}$

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

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 :

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

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

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

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

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

$\sf \longrightarrow Compound \: interest = 26620 - 20000$

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

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

▪︎Given:

➨Principal (P) = ₹ 20,000

➨Time (t) = 3 years

➨Rate of interest (R) = 10 %

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▪︎To Find :

➨What is the Difference between Compound Interest and Simple Interest

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▪︎Solution:-

✦To Find Simple interest,

➨Applying simple interest formula,

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{Simple \:Interest = \frac{P \times R \times t}{100} }}}}}$

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{Simple \:Interest = \frac{20000 \times 10 \times 3}{100} }}}}}$

$\longrightarrow \bigstar{ \underline{ \boxed{ \boxed{ \bf{ \red{Simple \:Interest = {6000} }}}}}}\bigstar$

✦To Find Compound Interest,

➨Applying Compound Interest formula,

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{ Compound\:Interest = P \: (1 + \frac{r}{100}) {}^{n} - P }}}}}$

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{ Compound\:Interest = 20000 \: (1 + \frac{10}{100}) {}^{3} - 20000 }}}}}$

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{ Compound\:Interest = 20000 \times (1 + \frac{10}{100}) {}^{3} - 20000 }}}}}$

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{ Compound\:Interest = 20000 \times ( \frac{10 + 100}{100}) {}^{3} - 20000 }}}}}$

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{ Compound\:Interest = 20000 \times \frac{1331000}{1000000} - 20000 }}}}}$

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{ Compound\:Interest = 20000 \times {1.331} - 20000 }}}}}$

$\longrightarrow \bigstar{ \underline{ \boxed{ \boxed{ \bf{ \red{ Compound\:Interest = 6620 }}}}}}\bigstar$

✦To Find Difference,

➨Subtract Simple Interest from Compound Interest,

$\longrightarrow{ \underline{ \boxed{ \boxed{ \sf{ Diffrence = 26620 - 20000 }}}}}$

$\longrightarrow \bigstar{ \underline{ \boxed{ \boxed{ \bf{ \red{ Diffrence =6620 }}}}}}\bigstar$

➨Hence The difference between Compound Interest and Simple Interest is ₹6620.

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