Four years ago, you bought a home with a purchase price of $$230,000$ and you paid $10\%$ of that amount as a down payment and financed the remainder. Your mortgage loan terms are $30$ years of monthly payments at an annual rate of $3\mathrm{.}60\%.$ Do no interim rounding on the calculated monthly interest rate.

$($a$)$ How much are your monthly mortgage payments?

$($b$)$ Over the life of the original loan, how much would you pay in interest?

$($c$)$ Remember that you took this loan out $4$ years ago $(48$ payments$).$ You got a new job and are moving across the country. You will be selling this house and looking at buying something new. Considering the $4$ years of payments you have made; how much do you still owe on your home?