A chemical facility is considering purchasing a new compressor. The price of the compressor is $$18500,$ the sales tax is $8\%,$ and the anonymous fee costs $$450.$ An investor offered to finance $90\%$ of the price of the compressor for $48$ months at a nominal interest rate of $9\%$ per year, compounded monthly. A deal is obtained between the investor and facility for the finance of $90\%$ of the price of the compressor.

a$)$ How much money does the facility need to pay at the time it purchases the compressor?

b$)$ How much is the monthly payment of facility to investor?