Answer:
The number of years it would take is [tex]n = 2 \ years[/tex]
Step-by-step explanation:
From the question we are told that
The earning per share is [tex]P =[/tex] $3.50
The growth rate is r = 7.0%
The duration is [tex]t = 5 \ years[/tex]
Generally the future value is mathematically represented as
[tex]A = P(1 + \frac{r}{100} )^n[/tex]
Where P is the present value
n is the time period
A is the future value which is mathematically evaluated as
[tex]A = 3 * P[/tex]
substituting value
[tex]A = 3 * 3.50[/tex]
[tex]A =[/tex] $ 10.5 0
So
[tex]A = P(1 + \frac{r}{100} )^n[/tex]
[tex]10.5 = 3.5(1 + \frac{7}{100} )^n[/tex]
[tex]10.5 = 3.225^n[/tex]
Taking log of both sides
[tex]log 10.5 = nlog 3.225[/tex]
[tex]1.0212 = n(0.5085)[/tex]
[tex]n = \frac{1.0212}{(0.5085)}[/tex]
[tex]n = 2 \ years[/tex]
