The question is: find the value of 500 dollars after 4 years invested at an annual interest rate of 9 percent (compounded continuously). I got 716.66. Is this correct? Thanks for your help!

Just to clarify something, since in my quest for help for this sort of problem on the internet, I found a few different formulas, the one that I am using is Pe^rt.

correct, good formula, good answer

To find the value of $500 after 4 years invested at an annual interest rate of 9 percent (compounded continuously), you can use the formula for continuous compound interest:

A = P * e^(rt)

Where:
A is the final amount (value after 4 years)
P is the initial principal (in this case, $500)
e is the mathematical constant approximately equal to 2.71828
r is the annual interest rate (in decimal form, so 9 percent becomes 0.09)
t is the time period in years (in this case, 4 years)

Plugging in the values, we get:

A = 500 * e^(0.09 * 4)

Using a calculator to evaluate e^(0.09 * 4), we get approximately 1.42725.

A = 500 * 1.42725
A ≈ 713.63

Therefore, the value of $500 after 4 years invested at an annual interest rate of 9 percent (compounded continuously) is approximately $713.63, not $716.66.

However, keep in mind that there may be slight differences in calculations due to rounding errors.