You are buying a house and the mortgage company offers to let you pay a "point"

(1.0 %

of the total amount of the loan) to reduce your APR from

6.46 %

to

6.21 %

on your

$ 403 comma 000

,

30

-year

mortgage with monthly payments. If you plan to be in the house for at least five years, should you do it? (Note: Be careful not to round any intermediate steps less than six decimal places.)

The monthly mortgage payment at 6.46% APR is:

The monthly mortgage payment at 6.21% APR is:

The lower interest rate on the mortgage results in monthly savings of:

The PV of the monthly savings is:

The balance of the mortgage at the end of five years at 6.46% APR is:

The balance of the mortgage at the end of five years at 6.21% APR is:

The principle reduction due to the lower interest rate is:

The PV of the principle reduction is:

The net benefit or cost is:

The net benefit is (positive or negative); therefore, you (should or should not) pay the point.