W998AMMT.7

7. You’ve found a $200,000 home that you want to buy. A mortgage broker gets you a 7% APR on a 30 year loan with monthly payments. Your first payment is due in one month.

• What will your monthly payments be? (5)

This is a straight-up annuity. PV=$200,000, r=.07, m=12, n=30, CF=?

• One option that the broker offers you is a point-paydown. You can pay an extra "point" equal to $2000 (1% of the mortgage value) in return for a lower rate on the loan, 6.75% APR.

If you are only planning to be in the house for 6 years, is this option a good deal? (6)

The paydown will get you lower payments, but the question is: will your savings on your payments add-up to enough so that paying $2000 for the savings is a good deal? Well, your new lower payments (which are still figured on a 30-year mortgage) will be:

but you will only plan on making 6 years worth (72) of them. Will the PV of your savings over 6 years be worth at least $2000? The difference between what your original payments are and your new payments are is $33.40 per month. The PV of 72 months of that savings is:

, so no, it is not a good deal.

• 6 years into the mortgage, you sell the house for $225,000. After you pay off your mortgage balance (assume your mortgage rate is the first one: 7% APR), how much of the proceeds from the sale will you be left with? (7)

 In order to pay-off your mortgage, you must give the bank an amount equal to the present value of all of the payments you still owe it. After 6 years, you still owe 360-72 = 288 payments of $1330.60. The PV (in year 6) of that stream is:

Leaving you with $225,000 - $185,382.41 = $39,617.59 from the sale.

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