Merve Dagdeviren financed her office furniture from a furniture dealer. The dealer$$s terms allowed her to defer payments $($including interest$)$ for three months and to make $24$ equal end of month payments thereafter. The original note was for $$18,000$ with interest rate at $6\%$ compounded monthly. After $16$ monthly payments, Merve found herself in a financial bind and went to a loan company for assistance. The loan company offered to pay her debts in one lump sum if she would pay the company $$350$ per month for the next $20$ months.

$($a$)$ Determine the original monthly payment made to the furniture store. $($b$)$ Determine the lump sum payoff amount the loan company will make.

$($c$)$ What monthly rate of interest is the loan company charging on this loan?