Question

The monthly payment p on a mortgage varies directly with the amount borrowed b. If the monthly payment on a 30-year mortgage is $6.94 for every $1,000 borrowed, find a linear equation that relates the monthly payment p to the amount borrowed b for a mortgage with the same terms. Then find the monthly payment p when the amount borrowed is $235,000.

Answer 1

Linear Modeling

The monthly payment p on a mortgage is a linear function of the amount borrowed B.

Two variables p and B are defined as proportional or with a direct variation if their quotient is constant.

For example, the cost of 1 apple is $0.35, the cost of two apples is $0.70, the cost of 10 apples is $3.50.

Here, the cost of N apples is proportional to N because the quotient is the same:

If we consider B as the independent variable and p as the dependent variable, then the equation is:

p = kB

Where k is the constant of proportionality

The second part of the question requires us to calculate the value of k. We use the provided data for that purpose. When B=$1,000, p=$6.94, thus:

6.94 = k*1,000

Then k = 6.94/1,000 = 0.00694

The equation is:

p = 0.00694B

If B=$235,000:

p = 0.00694*235,000

p = $1,630.90

The monthly payment is $1,630.90