I/ You plan to purchase a $500,000 home with a 20% down payment. You can take out a 30-year FRM of $400,000 at an APR of 7.2%.

(1) What is your monthly payment?

(2) If you make regular monthly payments, how long will it take to pay off half of the loan? (i.e., reduce the principle of the loan balance to half)

(3) After making regular monthly payments for 10 years, how much will be the loan balance?

Assume you obtain two quotes with and without (discount) points: either 7.2% APR without point or 6% with 2.5 points.

(4) For the 6% APR loan with 2.5 points, how much do you need to pay for the points?

(5) What is the NPV of paying the points? (i.e., the PV of savings in monthly payments over the life of the mortgage loan net of the initial payment for points)

(6) How long must you stay in the house to make it worthwhile to pay the points to lower down the interest rate, assuming the savings in payments can be reinvested at the same rate?