In order to accumulate enough money for a down payment on a house, a couple deposits $\$ 710$ per month into an account paying $3 \%$ compounded monthly. If payments are made at the end of each period, how much money will be in the account in 4 years? Type the amount in the account: $\$ \square$

Step 1 ：The couple is depositing a fixed amount every month into an account that compounds interest monthly. This is a case of future value of a series of payments or annuities. The formula for the future value of an annuity compounded monthly is: \(FV = P * [(1 + r/n)^(nt) - 1] / (r/n)\) where: \(FV\) is the future value of the annuity, \(P\) is the monthly 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, \(P = \$710\), \(r = 3\% = 0.03\), \(n = 12\) (since interest is compounded monthly), and \(t = 4\) years.

Step 3 ：We can substitute these values into the formula to find the future value of the annuity.

Step 4 ：\(P = 710\)

Step 5 ：\(r = 0.03\)

Step 6 ：\(n = 12\)

Step 7 ：\(t = 4\)

Step 8 ：\(FV = 36161.15797534041\)

Step 9 ：Final Answer: The amount in the account after 4 years will be \(\boxed{\$36161.16}\).