Consider a $30-$year, $$160,000$ mortgage with a rate of $6\mathrm{.}9$ percent. Eight years into the mortgage, rates have fallen to $5\mathrm{.}6$ percent.

Suppose the transaction cost of obtaining a new mortgage is $$1,700.$

a$.$ Should the homeowner refinance at the lower rate?

Yes

No

b$.$ Quantify the effect of the homeowner's decision.

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Monthly savings