Answered: When you use a mortgage to purchase a…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

When you use a mortgage to purchase a home, the lending 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(k) =

P((1 + r)^k − 1)

(1 + r)^t − 1

dollars.

In this exercise, assume that the mortgage amount is $200,000, the APR is 6%

so r = .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?

Halfway through the term of the mortgage corresponds to k₁ = _______ payments. From the graph, we see that E(k₁) is ________ half of the mortgage amount, so we _______ have half-ownership in the home halfway through the term of the mortgage.

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