Question

use $\text{pmt} = \dfrac{p\left(\dfrac{r}{n}\
ight)}{\left1 - \left(1 + \dfrac{r}{n}\
ight)^{-nt}\
ight}$ 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.

a. find the required down payment.
$23000

b. find the amount of the mortgage.
$\square$

Explanation:

Step1: Recall the relationship between home price, down payment, and mortgage amount.

The mortgage amount is the home price minus the down payment. The home price is $115,000 and the down payment (from part a) is $23,000.

Step2: Calculate the mortgage amount.

Let \( P_{\text{home}} = 115000 \) and \( P_{\text{down}} = 23000 \). Then the mortgage amount \( M = P_{\text{home}} - P_{\text{down}} \).
Substitute the values: \( M = 115000 - 23000 = 92000 \).

Answer:

\$92000