Question

at what rate of interest per annum 600 will become 661.50 in 2 years, the interest being compounded annually.​

Answer 1

Solution :

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

• Principal, (P) = Rs.600
• Amount, (A) = Rs.661.50
• Time, (n) = 2 years

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

The rate of the compounded annually.

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

Using formula of the compounded annually :

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

$\longrightarrow\sf{661.50=600\bigg(1+\dfrac{R}{100}\bigg)^{2}}\\\\\\\longrightarrow\sf{\dfrac{661.50}{600}=\bigg(1+\dfrac{R}{100}\bigg)^{2}}\\\\\\\longrightarrow\sf{\dfrac{661.50\times100 }{600\times 100}=\bigg(1+\dfrac{R}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\cancel{\dfrac{66150}{60000} }=\bigg(1+\dfrac{R}{100}\\\bigg)^{2}}\\\\\\\longrightarrow\sf{\cancel{\dfrac{2205}{2000}}=\bigg(1+\dfrac{R}{100}\bigg)^{2} }\\\\\\\longrightarrow\sf{\dfrac{441}{400}=\bigg(1+\dfrac{R}{100}\bigg)^{2} }$

$\longrightarrow\sf{\sqrt{\dfrac{441}{400} } =1+\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21}{20} =1+\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21}{20} -1=\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{21-20}{20} =\dfrac{R}{100} }\\\\\\\longrightarrow\sf{\dfrac{1}{20} =\dfrac{R}{100} }\\\\\longrightarrow\sf{20R=100}\\\\\longrightarrow\sf{R=\cancel{100/20}}\\\\\longrightarrow\bf{R=5\%}$

Thus;

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

Answer 2

Thus;

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