Question

A homeowner could take out a 15-year mortgage at a 5.5 percent annual rate on a $195,000 mortgage amount, or she could finance the purchase with a 30year mortgage at a 6.1 percent annual rate. How much total interest over the entire mortgage period could she save by financing her home with the 15-year mortgage (to the nearest dollar)?. ​

Answer 1

The total interest over the entire mortgage will be - $138,612

Mortgage amount = $195,000 (Given)

Annual Rate = 5.5%  (Given)

Therefore,

195,000 = Pmt × PVIFA (0.055/12, for 180 months)

= Pmt of 1,593.31 × 180 = 91,796;

= 195,000 = Pmt × PVIFA (0.061/12, for 360 months);

Pmt of 1,181.69 × 360 = 230,408;

Total Pmt will be -

= 230,408 - 91,796

= $138,612

Answer 2

As per the data given in the above question.

In the above question, it is given that,

The given data is mortgage amount $195000,

The annual rate is 5.5%

We have to find the total interest over the entire mortgage period.

Thus,

$195,000 = Pmt × PVIFA (0.055/12, for 180 months)= Pmt of 1,593.31 × 180 = 91,796;= 195,000 = Pmt × PVIFA (0.061/12, for 360 months);Pmt of 1,181.69 × 360 = 230,408;Total Pmt will be -= 230,408 - 91,796= 138,612$

Hence the total amount interest will be $138612.