How much must be deposited at the end of each month for 8 years to accumulate to $\mathrm{\$}3224.00$ at $12\mathrm{\%}$ compounded monthly?
The required deposit is $\mathrm{\$}$ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：The problem is asking for the monthly deposit needed to accumulate a certain amount after a certain period of time with a certain interest rate. This is a problem of future value of a series of payments, or an annuity.

Step 2 ：The formula for the future value of an annuity is: $FV=P\ast [(1+r/n{)}^{(}nt)-1]/(r/n)$ where: FV is the future value of the annuity, P is the amount of each payment, r is the annual interest rate (in decimal form), n is the number of times that interest is compounded per year, t is the time the money is invested for in years.

Step 3 ：In this case, we know FV ($3224), r (12% or 0.12), n (12 times per year), and t (8 years). We need to solve for P. Rearranging the formula to solve for P gives us: $P=FV\ast (r/n)/[(1+r/n{)}^{(}nt)-1]$

Step 4 ：We can plug in the known values and solve for P. FV = 3224, r = 0.12, n = 12, t = 8, P = 20.159160756581468

Step 5 ：Final Answer: The required monthly deposit is approximately $\boxed{{\displaystyle \mathrm{\$}20.16}}$