Answer:
$1,027.22
Step-by-step explanation:
To find the value of an initial investment of $800 after 10 years, with interest compounded continuously at a rate of 2.5%, we can use the continuous compounding interest formula:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Continuous Compounding Interest Formula}}\\\\A=Pe^{rt}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$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=800 e^{0.025\times 10}\\\\\\A=800 e^{0.25}\\\\\\A=800(1.2840254166...)\\\\\\A=1027.22033...\\\\\\A=1027.22[/tex]
Therefore, the value of the investment after 10 years is:
[tex]\Large\boxed{\boxed{\$1,027.22}}[/tex]
