Not only does Bill Smith need to start saving for his retirement, he just realized he has no savings for his daughter to attend college.$$ Assume the following:

Today is January $1,2025$ and Sally will start college on January $1,2033$ attending for five years

Total college expenses for $2033,$ payable in full on December $31,2033,$ is $$55,000.$ Each of the next four years of college expenses are payable on December $31$ for that given year.

College expenses are anticipated to increase $3\%$ from the prior year$$s cost $($college inflation$).$

Bill has set aside no savings for Sally$$s college as of January $1,2025$

Bill wishes to invest a fixed sum each month, starting January $31,2025$ and continuing for a total of $96$ months $($last payment December $31,2032)$ into an investment account that earns a fixed annual interest rate of $6\%$ during the entire savings$/$expenditure period.

What is the fixed monthly payment Bill must invest each month such the investment account will fund each annual amount of college expenses, leaving no amount left over and no need for Bill to make an additional payment subsequent to December $31,2031.$

Please show adequate details of your computation in an organized fashion