The formula $A=P e^{r t}$ gives the balance $A$ of an account earning what type of interest? The formula $A=P e^{r t}$ gives the balance $A$ of an account earning interest compounded daily. The formula $A=P e^{r t}$ gives the balance $A$ of an account earning interest compounded monthly. The formula $A=P e^{r t}$.gives the balance $A$ of an account earning interest compounded quarterly. The formula $A=P e^{r t}$ gives the balance $A$ of an account earning interest compounded continuously.

Step 1 ：The formula $A=P e^{r t}$ gives the balance $A$ of an account earning what type of interest?

Step 2 ：The formula $A=P e^{r t}$ is a mathematical representation of continuous compounding of interest. In this formula, $A$ is the final amount that will be achieved after time $t$, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal), and $e$ is the base of the natural logarithm, approximately equal to 2.71828.

Step 3 ：This formula is used when interest is compounded continuously, not daily, monthly or quarterly.

Step 4 ：Final Answer: The formula $A=P e^{r t}$ gives the balance $A$ of an account earning \(\boxed{\text{interest compounded continuously}}\).