Econ148.Mortgages.May31,10 - 1 Richard Arnott Economics 148...

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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 fixed-rate, fixed-term mortgage. The standard mortgage at the time was a thirty-year 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. 1
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This note was uploaded on 10/05/2010 for the course ECON 148 taught by Professor Richardarnott during the Spring '10 term at UC Riverside.

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Econ148.Mortgages.May31,10 - 1 Richard Arnott Economics 148...

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