The couple in problem #$2$ has the opportunity to take the same $$225,000$ loan for $15$ years at an interest rate of $2\mathrm{.}8\%$ compounded monthly.

a$)$ How much more$/$less than the original payment would the couple's new house payment be with this new offer?

b$)$ Would the couple save money in the long run or lose money in the long run with this option? How much? Should they do it$?$