Chapter 2.2, Problem 3E

Equity: When you use a mortgage to purchase a home, the leading institution effectively owns the home. You buy back part ownership in the home with each monthly payment. The part you have bought back is your equity in the home. If the mortgage amount is P dollars, the monthly interest rate is r as a decimal, and the term of the mortgage is t months, then your equity after k payments is

$E\left(k\right)=\frac{P\left({\left(1+r\right)}^k-1\right)}{{\left(1+r\right)}^t-1}\text{dollars}$

In this exercise, assume that the mortgage amount is $200,000, the APR is 6%(so $r=0.06/12$), and the term of the loan is 30 years (360 months).

a. Find a formula for the equity.

b. Make a graph of the equity over 360 months, the term of the loan.

c. Does the graph show that you have half-ownership in the home halfway through the term of the mortgage?