You bought a house a year ago for $$250,000,$ borrowing $$200,000$ at $10\%$ on a $30-$year term loan $($with monthly payments$).$ Interest rates have since come down to $9\%.$ You can refinance your mortgage at this rate, with a closing cost that will be $3\%$ of the loan. Your opportunity cost is $8\%.$ Ignore tax effects.

a$.$ How much are your monthly payments on your current loan $($at $10\%?$

b$.$ How would your monthly payments be if you could refinance your mortgage at $9\%($with a $30-$year term loan$)?$

c$.$ You plan to stay in this house for the next $5$ years. Given the refinancing cost of the loan$),$ would you refinance this loan?

d$.$ How much would interest rates have to go down before it would make sense to refinance this loan $($assuming that you are going to stay in the house for five years$)?$