Question

use $pmt = \frac{p\left(\frac{r}{n}\
ight)}{\left1 - \left(1 + \frac{r}{n}\
ight)^{-nt}\
ight}$ to determine the regular payment amount, rounded to the nearest dollar. the price of a home is $115,000. the bank requires a 20% down payment and three points at the time of closing. the cost of the home is financed with a 30-year fixed-rate mortgage at 7.5%. complete parts (a) through (e) below.
b. find the amount of the mortgage.
$ 92000
c. how much must be paid for the three points at closing?
$ 2760 (round to the nearest dollar as needed.)
d. find the monthly payment (excluding escrowed taxes and insurance)
$ 643 (round to the nearest dollar as needed.)
e. find the total cost of interest over 30 years
$\square$ (round to the nearest dollar as needed.)

Explanation:

Step1: Find total payments over 30 years

The monthly payment is $643, and there are \( 30 \times 12 = 360 \) months. So total payments are \( 643 \times 360 \).
\( 643 \times 360 = 231480 \)

Step2: Subtract mortgage amount to find interest

The mortgage amount (principal) is $92000. Total interest is total payments minus principal: \( 231480 - 92000 \).
\( 231480 - 92000 = 139480 \)

Answer:

\( 139480 \)