You are buying a house and the mortgage company offers to letyou 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 housefor at least five​ years, should you do​ it? ​(Note: Be careful notto round any intermediate steps less than six decimal​ places.)
The monthly mortgage payment at 6.46% APRis:
The monthly mortgage payment at 6.21% APRis:
The lower interest rate on the mortgage results inmonthly savings of:
The PV of the monthly savings is:
The balance of the mortgage at the end of five years at6.46% APR is:
The balance of the mortgage at the end of five years at6.21% APR is:
The principle reduction due to the lower interest rateis:
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.
