Problem $2$

A couple buying a house borrows $$225,000$ for $30$ years at $5\mathrm{.}4\%$ interest, compounded monthly.

a$)$ What is the couple's monthly house payment going to be$?$

b$)$ How much will the couple pay in interest?

c$)$ If the couple were to pay an additional $$125$ per month toward the cost of their home, how much sooner would the house be paid off?

d$)$ How much money in interest would doing this save the couple? Should they do it$?$