Question

what is the differences detween comopound interests for 2 years and 3 years for Rs. 500 at 10% rate compounded annually?​

Answer 1

Given

• Principal= Rs. 500
• Rate = 10%
• Time = 2 year's and 3 year's

To Find

• Differences detween comopound interests for 2 years and 3 years

Solution

$~~~~~~~~~\boxed{\sf \pink{CI= P\{\left( 1+\dfrac{R}{100}\right) ^{n} -1\}}}$

Compound Interest For 2 year's

${\implies \sf \: CI= 500\{\left( 1+\dfrac{10}{100}\right) ^{2} -1\}}$

${\implies\sf \: CI= 500\{\left(\dfrac{110}{100}\right) ^{2} -1\}}$

${\implies\sf \: CI= 500\{\left(\dfrac{11}{10}\right) ^{2} -1\}}$

${\implies\sf \: CI= 500\left(\dfrac{121}{100} - 1\right) }$

${\implies\sf \: CI= 500 \times \dfrac{121 - 100}{100}}$

${\implies\sf \: CI= 5 \times 21}$

$~~~~~~~ \boxed{\sf \: CI_{\pink{2 year's}}=Rs. 105}$

Now Compound Interest For 3 Years

${\implies \sf \: CI= 500\{\left( 1+\dfrac{10}{100}\right) ^{3} -1\}}$

${\implies \sf \: CI= 500\{\left(\dfrac{110}{100}\right) ^{3} -1\}}$

${\implies \sf \: CI= 500\{\left(\dfrac{11}{10}\right) ^{3} -1\}}$

${\implies \sf \: CI= 500\left(\dfrac{1331}{1000} - 1\right) }$

${\implies \sf \: CI= 500 \times \dfrac{1331 - 1000}{1000}}$

${\implies\sf \: CI= \dfrac{331}{2}}$

$~~~~~~~ \boxed{\sf \: CI_{\pink{3~ years}}= Rs. 165.5}$

• Differences detween compound interests for 2 years and 3 years = 165.5- 105 =Rs. 60.5