Question

Cheney is buying a house for $216,820. He made a down payment of $26,020 and will finance $190,800. He gets a 15 year fixed rate loan with a rate of 5.815%. How much interest will he pay over the life of his loan rounded to the nearest dollar?
A- $95,593
B- $134,649
C- $69,573
D- $108,629

Answer 1

The answer is letter A. $95,593.

Cheney has a monthly payment of $1,591.07 based on 5.815%.

Answer 2

The value of the Financing loan is PV=$190,800.

The Rate per month is 5.815%. Therefore, the Monthly Interest Rate,r = 0.4846%

We will use the formula:

$PV=PMT\times\frac{1-(1+r)^{-n}}{r}$

Where n=number of months in 15 years=12x15=180

and PMT=Payment every month, which is to be found.

Thus, $190800=PMT\times\frac{1-(1+\frac{0.4846}{100} )^{-180}}{\frac{0.4846}{100}}\approx PMT\times 119.92$

Thus $PMT=\frac{190800}{119.92}\approx 1591.1$

Thus, in 180 months Cheney pays: $1591.1\times 180\approx 286391$ dollars.

Thus Total Interest paid = $286,391 - $190,800= $95,590

Thus Option A is the closest correct option.