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...

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 yourequity in the home. If the mortgage amount isP dollars, the monthly interest rate isr as a decimal, and the term of the mortgage ist months, then your equity afterk 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 tok
₁
= _______ payments. From the graph, we see that
E(k
₁) is ________ half of the mortgage amount, so we _______ have half-ownership in the home halfway through the term of the mortgage.

Jun 05, 2022

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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...

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