The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


Example 10.2.7 Antoine and Maria earn a combined annual income of $76,500.
They are trying to qualify for a mortgage on a house for which the total monthly
payment (PITI) would be $1,494.57. Do they pass the 28% test?

Their gross monthly income is $76,500/12  $6,375; 28% of this is (0.28)($6,375) 
$1,785. Since the PITI is less than this, they PASS the 28% test.

The 28% rule is pretty simple, and there is a lot it does not take into account. In particular,
it does not take into account any other financial obligations. If Antoine and Maria have no
other debts, their situation is quite different than if they have two huge car loans, maxed out
credit cards, and enormous student loans to boot. A second rule commonly used rule takes
these other expenses into account:

The 36% Rule

To tal PITI and all other long-term debt payments cannot exceed 36% of
gross monthly income.

Long-term debt includes any debt with more than 1 year left in its term.

Just as with the 28% rule, not all lenders use the same percent for this type of test, and not
all lenders count the same things as long-term debt payments. In particular, some lenders
use 38% rather than 36% for this rule. However, the general idea is the same, even if the
specific details may vary.
The following example will illustrate how this rule is used.

Example 10.2.8 Suppose that Antoine and Maria (from the previous example) have
two car loans. The fi rst carries a monthly payment of $309.15 and has 2 years and
7 months left to go; the second has 6 months left to go and the monthly payment is
$175.14. They have student loan payments of $109.15 per month, and the minimum
monthly payments on their credit cards total $75.00. Do they pass the 36% test?

36% of their gross monthly income is (0.36)($6,375)  $2,295.00.

Their total debt payments would be $1,494.57  $309.15  $109.15  $75  $1,987.87.
(The second car loan is not included in this because less than 1 year remains in its term.) This
total is less than 36% of their monthly gross income, and so they PASS the 36% test as well.

Usually potential borrowers must pass both of these tests. If you pass one, but not the other,
you would not normally qualify for the mortgage. Antoine and Maria pass the income
qualification with no problem, and so assuming that everything else is in order they would
qualify for this mortgage easily.
An additional word of caution is called for here. The tests used by the lender are
designed to assess whether or not you are likely to be able to make the payments. They are
not designed to assess whether or not you will personally find the payments comfortable.
A PITI payment that you can afford may still eat up more of your income than you find
comfortable. The lender’s concern is: can you afford to make the payments? The lender is
not concerned with whether or not the payments will eat up so much of your income that
you don’t have money left to do other things that you might want to and buy other things
you might want to buy. Be careful not to confuse a lender’s determination of what you can
afford with your own assessment of what you can afford.

Up-Front Expenses


In addition to the monthly PITI payments, buying real estate usually involves a significant
cash outlay up front. Some of the many expenses involved include:

Down payment. As we have already discussed, you cannot normally borrow 100% of
the property’s value. Some down payment is required. Ordinarily, the minimum down
payment will be at least 3 to 5% of the price.
Legal fees. Home buyers often will hire an attorney to make sure that everything in the
transaction is done correctly. Even if you decide not to use an attorney, the mortgage
lender will have an attorney, and the borrower pays those fees.







10.2 Mortgages 441
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