Salom$$ and Gage take out a $30$ year mortgage for $$367,000$ at the APR of $8\mathrm{.}6\%,$ compounded monthly.

$($a$)$ What will their monthly payments be$?$

$($Round balance to the nearest cent.$)$

$

$($b$)$ After they had made $13$ years of the payments $(156$ payments$)$ they decide to refinance the remaining loan balance. What is the balance remaining on the original loan of $$367,000?$

$($Round balance to the nearest cent.$)$

$