when you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the…

when you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. the graph in the figure below shows for a certain 30 - year mortgage the equity, in dollars, accrued after a given number of monthly payments.\n(a) is the graph concave up or concave down?\nconcave up\nconcave down\n(b) the graph is increasing. what does the concavity you identified in part (a) say about how the equity grows?\nequity is decreasing at an increasing rate.\nequity is increasing at a decreasing rate.\nequity is increasing at an increasing rate.\nequity is not changing.\nequity is decreasing at a decreasing rate.\n(c) use the graph to estimate the amount of the mortgage.\n$

when you purchase a home by securing a mortgage, the total paid toward the principal is your equity in the home. the graph in the figure below shows for a certain 30 - year mortgage the equity, in dollars, accrued after a given number of monthly payments.\n(a) is the graph concave up or concave down?\nconcave up\nconcave down\n(b) the graph is increasing. what does the concavity you identified in part (a) say about how the equity grows?\nequity is decreasing at an increasing rate.\nequity is increasing at a decreasing rate.\nequity is increasing at an increasing rate.\nequity is not changing.\nequity is decreasing at a decreasing rate.\n(c) use the graph to estimate the amount of the mortgage.\n$

Answer

Explanation:

Step1: Determine concavity

A graph is concave up if the slope of the tangent line increases. Looking at the given graph of equity vs number - of monthly payments, as the number of monthly payments increases, the slope of the tangent line to the curve is increasing. So the graph is concave up.

Step2: Analyze growth based on concavity

Since the graph is increasing and concave up, the rate of change of the equity (the slope of the graph) is increasing. This means equity is increasing at an increasing rate.

Step3: Estimate mortgage amount

The initial equity is $0$. When the mortgage is fully paid off (at 360 months for a 30 - year mortgage), the equity is approximately $300000$. So the initial amount of the mortgage (when equity is $0$) is the value of the home, which we can estimate as the value of equity at the end of the mortgage term. So the amount of the mortgage is approximately $$300000$.

Answer:

(a) concave up (b) Equity is increasing at an increasing rate. (c) $300000$