May 31, 2010
Economics 148
Land and Resource Economics
Mortgages
One of the central themes of the course is the determination of land and housing rents and
values.
I have discussed a lot of real determinants: accessibility, construction technology,
amenities, uncertainty,  .
But I have not yet touched on an important financial
determinant – how an investor goes about obtaining the money to finance the purchase of
land or housing.
Increased availability of credit and better terms of credit increase the
demand for these assets, and therefore affects the price.
I am going to focus on the
residential mortgage market.
A residential mortgage loan is simply a loan collateralized by the residential property.
If
the buyer defaults on his loan payments, the lender has the right to take the property
(though he may prefer to renegotiate the loan – there are many options and the choice
between them is complicated).
The US has led the world in the development of its
mortgage market
1
.
The lender is called the mortgagor and the borrower the mortgagee.
Let us start with the mortgage that was most common up until about 1980, the fixedrate,
fixedterm mortgage.
The standard mortgage at the time was a thirtyyear mortgage (the
term
of the mortgage).
The mortgagee agrees to repay the loan in fixed monthly
payments over the thirty years of the mortgage. Suppose that a household buys a home
for $120,000 in 1970.
It makes a downpayment of 25% (the
downpayment rate
) of the
purchase price (which was typical for a first mortgage at the time), and finances the
remaining 75%, $90,000, with a mortgage, which it assumes on January 1, 1970, with a
mortgage interest rate of 5%.
I shall assume monthly compounding.
Using the
mortgage interest rate, the present value of the mortgage payments equals the amount of
the loan.
Letting M be the amount of the monthly payment, the first of which is due on
February 1, 1970 and the last, the 360
th
, on January 1, 2000, we have:
∑
i=1
360
M/(1 + r/12)
i
= 90000
(i)
We calculate M as follows:
∑
i=1
360
M/(1 + r/12)
i
=
∑
i=1
∞
M/(1 + r/12)
i

∑
i=361
∞
M/(1 + r/12)
i
= 12M/r – (12M/r)/(1 + r/12)
360
= (12M/r)(1 1/(1 + r/12)
360
)
= (240M)(1 – 0.2238) = 186.28M = 90000, so that M = $483.14
(ii)
Thus, the household makes a mortgage payment of $483.14 at the beginning of every
1
The
mortgage market
is the collection of institutions and individuals who are involved
in mortgage finance in one way or another.
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