Consider a $$600,000$ fixed rate mortgage with a $7\%$ interest rate, but instead the term is $15$ yrs$.$

a$.$ What is the monthly payment on thls loan?

b$.$ In the first month, how much principal is paid down and how much is paid in interest $($in dollar terme$)?$

c$.$ In what month do principal payments first exceed interest payments?

fo$.$ What is the remaining prihcipal balance after the $100$th payment?