Question

find the rate of compound interest per annum at which rs.800 becomes rs.882 in two years ​

Answer 1

Solution :

$\underline{\bf{Given\::}}}$

• Principal, (P) = Rs.800
• Amount, (A) = Rs.882
• Time, (n) = 2 years

$\underline{\bf{To\:find\::}}}$

The rate of the compound Interest .

$\underline{\bf{Explanation\::}}}$

Using formula of the compounded annually :

$\boxed{\bf{Amount=Principal\bigg(1+\frac{R}{100} \bigg)^{n} }}}}$

$\longrightarrow\sf{882=800\bigg(1+\dfrac{R}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\cancel{\dfrac{882}{800}} =\bigg(1+\dfrac{R}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\dfrac{441}{400} =\bigg(1+\dfrac{R}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{2\sqrt{\dfrac{441}{400} } =1+\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21}{20} -1=\dfrac{R}{100}} \\\\\\\longrightarrow\sf{\dfrac{21-20}{20} =\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{1}{20} =\dfrac{R}{100} }}$

$\longrightarrow\sf{20R=100}\\\\\longrightarrow\sf{R=\bigg(\cancel{\dfrac{100}{20} }\bigg)\%}\\\\\longrightarrow\bf{R=5\%}$

Thus;

The rate of the Interest will be R = 5% .