In $2024,$ Dr$.$ Chen$$s daughter is $8$ years old, and Dr$.$ Chen is planning for his daughter$$s college fund. He expects his daughter to start her college education at the age of $18,$ which is $10$ years from now. The expected cost of tuition only for a $4-$year college education in $2034$ is $$128,800($$$32,200$ per year$)$ at a public, in$-$state university. The college fund is invested to gain investment returns. Dr$.$ Chen is considering two investment options. The first is a mutual fund that is expected to provide an annual return of $8\%(0\mathrm{.}67\%$ per month$).$ The second is a bank deposit account that offers an annual return of $3\%(0\mathrm{.}25\%$ per month$).$ Dr$.$ Chen decides to put a fixed amount of money every month into the college fund starting from January $2024$ to January $2034(12$ months $\backslash$times $10$ years $=120$ months$).$ The interest is monthly compounded. With the mutual fund investment returns, if Dr$.$ Chen starts saving in January $2024,$ how much money does he need to put in every month to fully cover his daughter$$s college tuition if he wants the account fully funded when she turns $18?($Hint: There are $10$ full years left for Dr$.$ Chen to save for his daughter. We assume Dr$.$ Chen$$s daughter will do a four$-$year college with a fixed annual tuition of $$128,800($$$32,200$ per year$))$