Find the difference between the simple interest and the compound inter

1.	Find the difference between the simple interest and the compound interest on Rs. 8000 at 10% per annum for 3 years.
Answer» Given :- Principal = Rs. 8,000 Rate of interest = 10 % Time period = 3 years Required to find :- Difference between the simple Interest and the COMPOUND interest ? Formulae used :- $\large{\leadsto{\boxed{\rm{\bf{ Simple \; Interest = \dfrac{ PTR}{100} }}}}}$ $\large{\leadsto{\boxed{\rm{\bf{ A = {p \bigg[ 1 + \dfrac{R}{100} \bigg]}^{t} }}}}}$ Solution :- Given information :- Principal = Rs. 8,000 Rate of interest = 10 % Time period = 3 years we need to find the difference between the simple Interest and the compound interest . In order to find that , we should find what is the VALUE of simple interest & compound interest . So, Let's find the simple Interest ; Using the formula , $\large{\leadsto{\boxed{\rm{\bf{ Simple \; Interest = \dfrac{ PTR}{100} }}}}}$ $\longrightarrow{\tt{ SI = \dfrac{ 8,000 \times 10 \times 3 }{100} }}$ $\longrightarrow{\tt{ SI = \dfrac{ 8000 \times 30 }{ 100} }}$ $\longrightarrow{\tt{ SI = 80 \times 30 }}$ $\longrightarrow{\tt{ SI = 2400 }}$ Hence, Simple Interest = Rs. 2,400 Now, Let's find the compound interest ; Using the formula , $\large{\leadsto{\boxed{\rm{\bf{ A = {p \bigg[ 1 + \dfrac{R}{100} \bigg]}^{t} }}}}}$ Here, A = amount This implies ; $\leadsto{\sf{ A = 8000{ [ 1 + \dfrac{ 10 }{ 100 } ]}^{3} }}$ $\leadsto{\sf{ A = 8000 { [ 1 + \dfrac{1}{10} ]}^{3} }}$ $\leadsto{\sf{ A = 8000 { [ \dfrac{10 + 1 }{ 10 } ]}^{3} }}$ $\leadsto{\sf{ A = 8000 { [ \dfrac{11}{10} ] }^{3} }}$ $\leadsto{\sf{ A = 8000 \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10} }}$ $\leadsto{\sf{ A = 8 \times 11 \times 11 \times 11 }}$ $\leadsto{\sf{ A = 10,648 }}$ So, Amount = 10,648 But , we know that ; Compound interest = Amount - principal => 10,648 - 8,000 => Rs. 2,648 Hence, Compound interest = Rs. 2,648 Now, Let's find the difference between the SI and CI ( SI - Simple Interest , CI = Compound Interest ) This implies ; Compound Interest - Simple Interest => 2,648 - 2,400 => Rs. 248 Therefore, The difference between the simple Interest and the compound interest = Rs. 248