To calculate the final amount of money at the end of the period, considering that the interest is compounded continuously you have to use the following formula:
[tex]A=P\cdot e^{rt}[/tex]Where
A is the accrued amount at the end of the given time
P is the principal amount
r is the annual nomial interes expressed as a decimal value
t is the time period in years
For this investment, the initial value is P= $200
The interest rate is 6%, divide it by 6 to express it as a decimal value
[tex]\begin{gathered} r=\frac{6}{100} \\ r=0.06 \end{gathered}[/tex]The time is t= 20 years
[tex]\begin{gathered} A=200\cdot e^{0.06\cdot20} \\ A=200\cdot e^{\frac{6}{5}} \\ A=664.02 \end{gathered}[/tex]After 20 years, the amount of money in the account will be $664.02
