Consider a $30-$year, $$230,000$ mortgage with a rate of $6\mathrm{.}90$ percent. Five years into the mortgage, rates have fallen to $5\mathrm{.}70$ percent. Suppose the transaction cost of obtaining a new mortgage is $$2,500.$

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

multiple choice

Yes

No

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