Answer:
$19,287.13
Step-by-step explanation:
To find the amount in a continuously compounded account after 30 years, we can use the continuous compounding interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Continuous Compounding Interest Formula}}\\\\A=Pe^{rt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$A$ is the final amount.}\\\phantom{ww}\bullet\;\;\textsf{$P$ is the principal amount.}\\\phantom{ww}\bullet\;\;\textsf{$e$ is Euler's number (constant).}\\\phantom{ww}\bullet\;\;\textsf{$r$ is the interest rate (in decimal form).}\\\phantom{ww}\bullet\;\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]
In this case:
- P = $5000
- r = 4.5% = 0.045
- t = 30 years
Substitute the values into the formula and solve for A:
[tex]A=5000\cdot e^{0.045 \cdot 30}[/tex]
[tex]A=5000\cdot e^{1.35}[/tex]
[tex]A=5000\cdot 3.85742553...[/tex]
[tex]A=19287.12765348...[/tex]
[tex]A=19287.13[/tex]
Therefore, the amount in the continuously compounded account after 30 years would be $19,287.13.
