In what time will Rs 64000 amounts to Rs 68921 at 5% per annum interest being compounded half yearly ?

11¹/₂ years
22 years
33 years
42¹/₂ years

Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to the question \\ Amount = {(1 + \frac{R}{2 \times 100})}^{2 \times t} \\ \Rightarrow 68921 = 64000 {(1 + \frac{5}{2 \times 100})}^{2 \times t} \\ \Rightarrow \frac{68921}{64000} = {(1 + \frac{1}{40})}^{2 \times t} \\ \Rightarrow {(\frac{41}{40})}^{3} = {(\frac{41}{40})}^{2 \times t} \\ \Rightarrow 2 t = 3 \\ \Rightarrow t = \frac{3}{2} \\ \Rightarrow t  =  1 \frac{1}{2} years \end{aligned}

$\eqalign{ & {\text{According to the question}} \cr & {\text{Amount}} = {\text{ }}{\left( {1 + \frac{{\text{R}}}{{2 \times 100}}} \right)^{2 \times {\text{t}}}} \cr & \Rightarrow 68921 = 64000{\left( {1 + \frac{5}{{2 \times 100}}} \right)^{2 \times {\text{t}}}} \cr & \Rightarrow \frac{{68921}}{{64000}} = {\left( {1 + \frac{1}{{40}}} \right)^{2 \times {\text{t}}}} \cr & \Rightarrow {\left( {\frac{{41}}{{40}}} \right)^3} = {\left( {\frac{{41}}{{40}}} \right)^{2 \times {\text{t}}}} \cr & \Rightarrow 2{\text{t = 3}} \cr & \Rightarrow {\text{t = }}\frac{3}{2} \cr & \Rightarrow {\text{t = 1}}\frac{1}{2}{\text{ years}} \cr}$