How do I find the effective annual interest rate?

Suppose that a bank provides an annual interest rate of 8% that is compounded continuously. Determine the effective annual interest rate (in percentage).





I know that the effective annual interest rate is an amount being compounded annually instead of being compounded continuously but I still can't figure this out. Help would be appreciated.|||Whenever you're asked to find an equivalent rate, you need to set the accumulated value of $1 at one rate equal to the accumulated value of $1 at the rate you're solving for. Both accumulated values must be over the same time period.





Let i = effective annual interest rate.





The accumulated value of $1 at the end of 1 year at effective annual interest rate i is 1 + i.





The accumulated value of $1 at the end of 1 year at continuous interest rate 8% is e^(.08).





Setting the accumulated values equal to each other:


1 + i = e^(.08)


i = e^(.08) - 1 = 0.083287068





Therefore, the effective annual interest rate is 8.3287068%.|||To convert this into an annual rate, use $1 as your original investment, and calculate the continuous interest after 1 year.





Your answer minus the original dollar will give you your effective annual rate. I'm getting: 8.3237% (but I used an internet calculator, you might want to do it long-hand to check my work.