b. Find the interest.
\begin{tabular}{|l|l|l|}
\hline Periodic Deposit & Rate & Time \\
\hline 570 at the end of each month & $4 \%$ compounded monthly & 40 years \\
\hline
\end{tabular}
(i) Click the icon to view some finance formulas.
a. The value of the annuity is $\$$
(Do not round until the final answer. Then round to the nearest dollar as needed.)
b. The interest is $\$$
(Use the answer from part (a) to find this answer. Round to the nearest dollar as needed)

Step 1 ：Given a periodic deposit of $570 at the end of each month for 40 years with a rate of 4% compounded monthly, we are asked to find the interest earned.

Step 2 ：We first calculate the future value of the annuity using the formula for the future value of an ordinary annuity: \(FV = P \times \left[(1 + \frac{r}{n})^{nt} - 1\right] / \left(\frac{r}{n}\right)\), where \(FV\) is the future value of the annuity, \(P\) is the periodic deposit, \(r\) is the annual interest rate (in decimal form), \(n\) is the number of times the interest is compounded per year, and \(t\) is the time the money is invested for in years.

Step 3 ：Substituting the given values into the formula, we get \(FV = 570 \times \left[(1 + \frac{0.04}{12})^{12 \times 40} - 1\right] / \left(\frac{0.04}{12}\right)\), which simplifies to \(FV = 673717.963794993\).

Step 4 ：We then calculate the total amount of deposits made over the 40 years, which is \(570 \times 12 \times 40 = 273600\).

Step 5 ：Finally, we find the interest by subtracting the total amount of deposits from the future value of the annuity, which is \(673717.963794993 - 273600 = 400118\).

Step 6 ：So, the interest earned is \(\boxed{400118}\) dollars.