Question

At what rate of compound interest per annum will a sum of rs.1200 becomes rs.1348.32 in 2 years

A) 66%% B) 6.5% C) 7% D) 7.5%

Answer 1

S O L U T I O N :

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

• Amount, (A) = Rs.1348.32
• Principal, (P) = Rs.1200
• Time, (T) = 2 years

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

The rate of the compound Interest.

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

Let we suppose rate be r

Using formula :

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

$\underbrace{\sf{Accoding\:to\:the\:question\::}}}}}$

$\longrightarrow\sf{1348.32=1200\bigg(1+\dfrac{r}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\dfrac{1348.32}{1200} =\bigg(1+\dfrac{r}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\dfrac{1348.32\times 100}{1200\times 100} =\bigg(1+\dfrac{r}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\cancel{\dfrac{134832}{120000}} =\bigg(1+\dfrac{r}{100} \bigg)^{2} }\\\\\\\longrightarrow\sf{\dfrac{44944}{40000} =\bigg(1+\dfrac{r}{100} \bigg)^{2} }$

$\longrightarrow\sf{\sqrt{\dfrac{44944}{40000}} =1+\dfrac{r}{100} }\\\\\\\longrightarrow\sf{\dfrac{212}{200} =1+\dfrac{r}{100} }\\\\\\\longrightarrow\sf{\dfrac{212}{200} -1=\dfrac{r}{100} }\\\\\\\longrightarrow\sf{\dfrac{212-200}{200} =\dfrac{r}{100} }\\\\\\\longrightarrow\sf{\dfrac{12}{200} =\dfrac{r}{100} }\\\\\\\longrightarrow\sf{200r=1200\:\:\underbrace{\sf{Cross-multiplication}}}\\\\\\\longrightarrow\sf{r=\cancel{\dfrac{1200}{200} }}\\\\\\\longrightarrow\bf{r=6\%}$

Thus;

The rate of the compound Interest will be 6% .