The compound interest on Rs. 30000 at 7% per annum is Rs. 4347. The period (in years) is = ?

12 years
22 ¹/₂ years
33 years
44 years

Answer:- 1

Explanation:-

Solution:

\begin{aligned} =  Rs . (30000 - 4347) \\ Rs . = 34347 \\ Let the time be n years \\ Then, \\ 30000 {(1 + \frac{7}{100})}^{n} = 34347 \\ \Leftrightarrow {(\frac{107}{100})}^{n} = \frac{34347}{30000} \\ \Leftrightarrow {(\frac{107}{100})}^{n} = \frac{11449}{10000} = {(\frac{107}{100})}^{2} \\ ∴ n = 2 years \end{aligned}

$\eqalign{ & {\text{ = Rs}}{\text{. }}\left( {30000 - 4347} \right) \cr & {\text{Rs}}{\text{.}} = 34347 \cr & {\text{Let the time be }}n{\text{ years}} \cr & {\text{Then,}} \cr & {\text{30000}}{\left( {1 + \frac{7}{{100}}} \right)^n} = 34347 \cr & \Leftrightarrow {\left( {\frac{{107}}{{100}}} \right)^n} = \frac{{34347}}{{30000}} \cr & \Leftrightarrow {\left( {\frac{{107}}{{100}}} \right)^n} = \frac{{11449}}{{10000}} = {\left( {\frac{{107}}{{100}}} \right)^2} \cr & \therefore n = {\text{ 2 years}} \cr}$