The compound interest on Rs. 30000 at 7% per annum for a certain time is Rs. 4347. The times is = ?

13 years
24 years
32 years
42.5 years

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Principal  =  Rs . 30000 \\ CI  =  Rs 4347 \\ Rate  =  7 % \\ By using formula, \\ \Rightarrow (30000 + 4347) = 30000 {(1 + \frac{7}{100})}^{t} \\ \Rightarrow 34347 = 30000 {(1 + \frac{7}{100})}^{t} \\ \Rightarrow \frac{34347}{30000} = {(\frac{107}{100})}^{t} \\ \Rightarrow (\frac{11449}{10000}) = {(\frac{107}{100})}^{t} \\ \Rightarrow {(\frac{107}{100})}^{2} = {(\frac{107}{100})}^{t} \\ \Rightarrow t = 2 years \end{aligned}

$\eqalign{ & {\text{Principal = Rs}}{\text{. 30000}} \cr & {\text{CI = Rs 4347}} \cr & {\text{Rate = 7}}\% \cr & {\text{By using formula, }} \cr & \Rightarrow \left( {30000 + 4347} \right) = 30000{\left( {1 + \frac{7}{{100}}} \right)^{\text{t}}} \cr & \Rightarrow 34347 = 30000{\left( {1 + \frac{7}{{100}}} \right)^{\text{t}}} \cr & \Rightarrow \frac{{34347}}{{30000}} = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr & \Rightarrow \left( {\frac{{11449}}{{10000}}} \right) = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr & \Rightarrow {\left( {\frac{{107}}{{100}}} \right)^2} = {\left( {\frac{{107}}{{100}}} \right)^{\text{t}}} \cr & \Rightarrow {\text{t}} = 2\,{\text{years}} \cr}$