Jessie Broughton owns property in Tofino with a $$150,000$ original mortgage on it$.$ Jessie would like to release some equity for renovations and is looking for refinancing. He is considering paying out the existing mortgage and replacing it with a new first mortgage at current rates and conditions. The existing mortgage began $4$ years ago with a $5-$year term and a $25-$year amortization. The loan has monthly payments at an interest rate of $8\%$ per annum, compounded semi$-$annually. There is no prepayment penalty.

The Tofino Trust Company has $5-$year term mortgage loans available. The loan has a $20-$year amortization period, monthly payments, and an interest rate of $2\mathrm{.}75\%,$ compounded semi$-$annually. They use an $80\%$ loan$-$to$-$value ratio constraint. The Trust Company has assigned a lending value of $$200,000$ to Jessie's $2,200$ square foot house.

$($a$)$

What is the maximum loan Jessie will be able to obtain from the Tofino Trust Company if he does not want his monthly payments to exceed $$1,000?$

$($b$)$ If he takes the maximum loan available to him from the Tofino Trust Company, by how much does Jessie's monthly debt service change?