Answer:
$8,706.57
Step-by-step explanation:
To calculate the future value of a $4,500 investment compounded continuously at an annual interest rate of 6.6%, we can use the Continuous Compounding Interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Continuous Compounding Interest Formula}}\\\\A=Pe^{rt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$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:
Substitute the values into the formula and solve for A:
[tex]A=4500 \cdot e^{0.066 \cdot 10}\\\\\\A=4500 \cdot e^{0.66}\\\\\\A=4500 \cdot 1.9347923344...\\\\\\A=8706.5655048...\\\\\\A=8706.57[/tex]
Therefore, the amount of money in the account after 10 years will be $8,706.57.