Question

A homeowner could take out a 15 year mortgage at a 3.5% annual rate on a $250,000 mortgage amount or she could refinance the purchase with a 30 year mortgage at a 4% annual rate. How much total interest over the entire mortgage periods could she save by financing her home with a 15 year mortgage to the nearest dollar? 1.) 130,408 2.) 110,105 3.)107,977 4.) 95,107 5.) 150,250

Answer 1

Case-1 15yr Mortgage
Amount borrowed				250000
Annual rate				3.50%
Monthly rate (3.5/12) = 0.2917%
Annuity PVF at 0.2917% for 180 periods				139.8793
Monthly payment (250000/139.87928)				1787.26
Total Amount paid (1787.26*180)				321706.8
Less: Loan borrowed				250000
Total Interest paid				71706.8
Case-2 30 yr Mortgage
Amount borrowed				250000
Annual rate				4.00%
Monthly rate (4/12) = 0.0.333%
Annuity PVF at 0.333% for 360 periods				209.5625
Monthly payment (250000/209.5625)				1192.96
Total Amount paid (1192.96*360)				429465.6
Less: Loan borrowed				250000
Total Interest paid				179465.6
Total Savings in Interest = 179465.6- 71706.8 =107758
Answer is 3. $ 107977
Note: The difference of amount is just because of rounding off the PVF