Question

find the difference in the simple interest and compound interest on rs 645 for 2 years at the rate of 6% PA​

Answer 1

To Find :-

The difference between the Simple interest and the compound interest.

We know :-

Simple Interest :-

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

Where :-

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

Amount :-

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

Where :-

• A = Amount
• P = Principal
• R = Rate of Interest
• n = Time Perio

Compound :-

$\over{\boxed{\underline{\bf{CI = A - P}}}}$

Where :-

• CI = Compound Interest
• A = Amount
• P = Principal

Solution :-

Simple Interest :

Given :-

• P = Rs. 645

• R = 6% p.a.

• t = 2 years

Using the formula and substituting the values in it , we get :-

$:\implies \bf{SI = \dfrac{P \times R \times t}{100}} \\ \\ \\ :\implies \bf{SI = \dfrac{645 \times 6 \times 2}{100}} \\ \\ \\ :\implies \bf{SI = \dfrac{645 \times 6 \times 1}{50}} \\ \\ \\ \bf{SI = \dfrac{645 \times 3 \times 1}{25}} \\ \\ \\ \bf{SI = \dfrac{1935}{25}} \\ \\ \\ \bf{SI = 77.4} \\ \\ \\ \purple{\bf{SI = 77.4}}$

Hence, the Simple interest is Rs. 77.4 .

Compound Interest :-

Amount :-

Given :-

• P = Rs. 645

• R = 6% p.a.

• t = 2 years

Using the formula and substituting the values in it , we get :-

$:\implies \bf{A = P\bigg(1 + \dfrac{R}{100}\bigg)^{n}} \\ \\ \\ :\implies \bf{A = 645\bigg(1 + \dfrac{6}{100}\bigg)^{2}} \\ \\ \\ :\implies \bf{A = 645\bigg(\dfrac{106}{100}\bigg)^{2}} \\ \\ \\ :\implies \bf{A = 645\bigg(\dfrac{100 + 6}{100}\bigg)^{2}} \\ \\ \\ :\implies \bf{A = 645\bigg(\dfrac{106}{100}\bigg)^{2}} \\ \\ \\ :\implies \bf{A = 645 \times \dfrac{106}{100} \times \dfrac{106}{100}} \\ \\ \\ :\implies \bf{A = 645 \times \dfrac{53}{50} \times \dfrac{53}{50}} \\ \\ \\ :\implies \bf{A = 129 \times \dfrac{53}{10} \times \dfrac{53}{50}} \\ \\ \\ :\implies \bf{A = \dfrac{129 \times 53 \times 53}{10 \times 50}} \\ \\ \\ :\implies \bf{A = \dfrac{362361}{500}} \\ \\ \\ :\implies \bf{A = 724.9} \\ \\ \\ \purple{\bf{A = 724.7}}$

Hence, the amount is Rs. 724.7.

Compound interest = A - P

==> CI = 724.7 - 645

==> Rs. 79.7

Hence, the compound interest is Rs. 79.7.

Difference between the compound interest and simple Interest :-

==> CI - SI

==> 79.7 - 77.4

==> R.s 2.3

Hence, the difference between the Compound Interest and the simple Interest is 2.3 .