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?

multiple choice:

Yes

No

B$.)$ Quantify the effect of the homeowner's decision.

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