Answer:
An yearly interest rate of 7.57% is needed to be for this to be possible.
Step-by-step explanation:
The amount of money after t years of continuous compounding is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial investment and r is the interest rate, as a decimal.
In this problem, we have that:
[tex]P(0) = 200, P(6) = 315[/tex]
We have to find r.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]315 = 200e^{6r}[/tex]
[tex]e^{6r} = \frac{315}{200}[/tex]
[tex]\ln{e^{6r}} = \ln{\frac{315}{200}}[/tex]
[tex]6r = \ln{\frac{315}{200}}[/tex]
[tex]r = \frac{\ln{\frac{315}{200}}}{6}[/tex]
[tex]r = 0.0757[/tex]
An yearly interest rate of 7.57% is needed to be for this to be possible.
