$($a$)$ The amount of money one would pay each month on a loan of $$225,000$ at an interest rate of $4\%$ over $30$ years $(360$ months$).($Note: this only includes the payment on the debt, not insurance, etc.$)$

$($b$)$ The amount of time it would take to pay the loan off $($in months$)$ if that payment were increased $$100$

$($c$)$ Using the payment in part $($a$)$ Calculate the balance of the ORIGINAL loan after the time calculated in part $($b$).$

Could you answer a$,$ b$,$ and c$?$