Question #$1$

You decided to buy a house worth $$500,000.$ You financed your house with a $15-$year fixed$-$rate monthly mortgage with an APR of $6\%.$

A$.$ Calculate the monthly payment on your mortgage.

B$.$ How much interest will you pay over the course of the loan?

C$.$ Consider the situation where, after $5$ years you decide to pay off your mortgage. What it means that at the end of $5$ years $(60$ months$)$ you make a lump sum payment called a "balloon" or a "bullet" to pay off the remaining balance of your loan. How big will the balloon payment be$?$

D$.$ Calculate the present value of an annuity where you are paying the monthly fixed amount that you calculated in part A for a period of $10$ years $(120$ months$).$ The APR is still $6\%.$

E$.$ Accounting for rounding errors, is your answer from part $D$ different from what you calculated in part C$?$ Please explain "why" or "why not?"