An automobile loan of $$15,000$ at an effective annual interest rate of $6\mathrm{.}17\%$ or a monthly interest rate of $0\mathrm{.}5\%,$ compounded monthly for $36$ months, requires

equal end$-$of$-$month payments.

$($a$)$ Calculate the monthly payments for the loan

$($b$)$ Complete the following table for the first $3$ payments.