How much will Maria and Raul have to deposit each month into an annuity that earns $4.5 \%$, if they want to have $\$ 55,000.00$ in 16 years? Assume the interest rate does not change while the account is open. Round your fina answers to the nearest cent. How much interest, in total, will they earn? CHECK ANSWER Attempt 2 of 3

Step 1 ：The problem is asking for the monthly deposit amount into an annuity, given the future value, interest rate, and time period. The formula for the monthly deposit (PMT) when interest is compounded monthly is: \(PMT = \frac{FV * r/n}{(1 + r/n)^{nt} - 1}\) where: PMT is the monthly deposit, FV is the future value ($55,000 in this case), r is the annual interest rate (4.5% or 0.045 in this case), n is the number of times interest is compounded per year (12 times in this case, since it's compounded monthly), t is the time in years (16 years in this case).

Step 2 ：We can plug in the given values into this formula to find the monthly deposit. \(FV = 55000\), \(r = 0.045\), \(n = 12\), \(t = 16\)

Step 3 ：Calculate the monthly deposit: \(PMT = \frac{55000 * 0.045/12}{(1 + 0.045/12)^{12*16} - 1}\)

Step 4 ：Final Answer: The amount of money that Maria and Raul should deposit each month is approximately \(\boxed{174.94}\).