$($a$)$ You took out a $30-$year mortgage $($monthly payments$)$ for $155,000$ at $7\mathrm{.}3\%$ and payment number $60$ has just been paid today. You are deciding whether you should refinance the outstanding principal by borrowing at today$$s lower rate of $5\mathrm{.}8\%$ an amount that just pays off the old loan. The new loan is for $30$ years as of today. The total fees for getting the new loan equal $3\mathrm{.}5\%$ of the borrowed principal, and you will pay the fees today with funds from your savings account.

i$)$ How much would you save in terms of monthly payments if you refinance?

ii$)$ How much do you save in today$$s terms?

iii$)$ How much must the rate of the new loan change to make refinancing undesirable? Use $6+$ decimals.