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 $150,000, 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. E(k) =
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 $150,000, 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. E(k) =
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Mortgages
A mortgage is a formal agreement in which a bank or other financial institution lends cash at interest in return for assuming the title to the debtor's property, on the condition that the obligation is paid in full.
Mortgage
The term "mortgage" is a type of loan that a borrower takes to maintain his house or any form of assets and he agrees to return the amount in a particular period of time to the lender usually in a series of regular equally monthly, quarterly, or half-yearly payments.
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) =
dollars.| P((1 + r)k − 1) |
| (1 + r)t − 1 |
In this exercise, assume that the mortgage amount is $150,000, the APR is 6%
so r =
,
and the term of the loan is 30 years (360 months).
| 0.06 |
| 12 |
(a)
Find a formula for the equity.
E(k) =
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