Dillon and Cassie bought their house twelve years ago for $$275,000.$ Their mortgage is a $30-$year mortgage at $4\mathrm{.}75\%$ interest compounded monthly.

a$.$ What is the amount of their monthly payments?

b$.$ What is the current balance on their loan?

They have the option to refinance the mortgage at $2\mathrm{.}875\%$ for $20$ years and are considering whether it would be a good idea.

c$.$ If they choose to refinance, what would their payments be for the new mortgage? $(3)$ They like the idea of the lower payment but are also concerned that this option would mean that it would take two additional years to pay off the mortgage.

d$.$ If they stay with their original loan, what will be the total amount of money paid $($principal and interest$)$ over the remaining eighteen years of the loan?

e$.$ If they refinance, what will be the total amount of money paid $($principal and interest$)$ over the twenty years of the loan?

Dillon$$s dad suggests that they refinance their mortgage at the new rate, and then instead of making the new lower payment, they continue making the original payment amount on the new loan.

f$.$ If they choose this option, how long will it take for them to pay off the loan?

g$.$ If they choose this option, what would be the total amount of money paid $($principal and interest$)$ until the loan is paid off?