Question

find the compound interest on rupees 8000 at 15% for 1 year, if the interest is compounded semi annually? ​

Answer 1

Given :-

• Principal = ₹8000
• Rate% = 15%
• Time = 1 year

Aim :-

• To find the compound interest, if the interest is compounded semi - annually/half yearly

Answer :-

Formula to use :-

$\boxed {\sf \longrightarrow amount = principal \bigg(1 + \dfrac{rate}{200} \bigg)^{2 \times time} }$

$\boxed {\sf \longrightarrow compound \: interest = amount - principal}$

Solution :-

Substituting the values,

$\implies \sf amount = 8000 \bigg( 1 + \dfrac{15}{200} \bigg)^{2 \times 1}$

Taking the LCM as 200,

$\implies \sf amount = 8000\bigg(\dfrac{200 + 15}{200} \bigg)^{2 }$

$\implies \sf amount = 8000 \bigg( \dfrac{215}{200} \bigg ) ^{2}$

Reducing to the lowest terms,

$\implies \sf amount = 8000 \bigg( \cfrac{43}{40} \bigg)^{2}$

$\implies \sf amount = 8000 \times \dfrac{43}{40} \times \dfrac{43}{40}$

Cancelling the zeros,

$\implies \sf amount = 80 \not0 \not0 \times \dfrac{43}{4 \not0} \times \dfrac{43}{4 \not0}$

Reducing to the lowest terms, we get :-

$\implies \sf amount = 5 \times 43 \times 43$

$\implies \sf amount = 9245$

Now that we have the value of the amount, the compound interest will be :-

$\implies \sf compound \: interest = amount - principal$

$\implies \sf compound \: interest = 9245 - 8000$

$\implies \sf compound \: interest = 1245$

Hence, compound interest on ₹8000 is ₹1,245

Some more formulas :-

• Simple interest :-

$\longrightarrow \sf simple \: interest = \dfrac{principal \times rate \times time}{100}$

• When interest is compounded quarterly :-

$\longrightarrow \sf amount = principal \bigg(1 + \dfrac{rate}{400} \bigg)^{4 \times time}$

• When interest is compounded annually/yearly :-

$\longrightarrow \sf amount = principal \bigg(1 + \dfrac{rate}{100} \bigg) ^{ time }$