ANSWER
[tex]\begin{gathered} (1)\text{ }\$56,894.43 \\ \\ (2)\text{ }17.33\text{ years} \end{gathered}[/tex]EXPLANATION
(1) The formula for the amount for a continuously compounded interest is given by:
[tex]A=Pe^{rt}[/tex]where P = principal (initial amount) = $30000
r = interest rate = 4% = 0.04
t = number of years
To find the amount he has after 16 years, find the value of A when t is 16:
[tex]\begin{gathered} A=30000*e^{0.04*16} \\ \\ A=30000*e^{0.64} \\ \\ A\approx\$56,894.43 \end{gathered}[/tex]That is the amount in the account after 16 years.
(2) To find how long it takes for the money to double, we have to find t when A is $60000:
[tex]\begin{gathered} 60000=30000*e^{0.04t} \\ \\ \frac{60000}{30000}=e^{0.04t} \\ \\ 2=e^{0.04t} \\ \\ \ln2=\ln e^{0.04t} \\ \\ 0.04t=\ln2 \\ \\ t=\frac{\ln2}{0.04} \\ \\ t\approx17.33\text{ years} \end{gathered}[/tex]That is the time that it will take for the money to double.
