In order to accumulate enough money for a down payment on a house, a couple deposits $\$ 428$ per month into an account paying 6\% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 6 years?
What is the amount in the account after 6 years?
(Round to the nearest cent as needed.)

Step 1 ：This problem involves calculating the future value of a series of regular deposits in an account with compound interest. The formula for this is: \(FV = P \times \left[(1 + \frac{r}{n})^{nt} - 1\right] \div \frac{r}{n}\), where FV is the future value of the investment/loan, including interest, P is the regular deposit (payment), r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.

Step 2 ：In this case, the regular deposit, P, is $428, the annual interest rate, r, is 6% or 0.06 in decimal form, the number of times interest is compounded per year, n, is 12 (since it's compounded monthly), and the time the money is invested for, t, is 6 years.

Step 3 ：Substituting these values into the formula, we get: \(FV = 428 \times \left[(1 + \frac{0.06}{12})^{12 \times 6} - 1\right] \div \frac{0.06}{12}\)

Step 4 ：Solving this expression gives a future value, FV, of approximately $36982.99.

Step 5 ：\(\boxed{36982.99}\) is the amount that will be in the account after 6 years.