The Mathematics of Money

(Darren Dugan) #1

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


This can be easily confused with a similar financial product called a home equity line of
credit. The difference between the two is that, with a home equity line, instead of being lent
a set amount up front, the borrowers are given a checkbook or debit card that they can use
to borrow money as needed against their home equity up to a set limit.
Occasionally, some finance companies will offer mortgage loans for more than the value
of the property. In those cases, it is actually possible to have negative equity in a property.
(Owing more against something than its value is sometimes referred to as being upside-
down with the loan.) The following example will illustrate:

Example 10.2.2 Suppose that Les and Rhonda from the previous example are
offered a loan by a company that will allow them to borrow up to a maximum of 125%.
How much could they borrow with this loan, and what would their equity be if they did?

Les and Rhonda could have a maximum mortgage debt of

(1.25)($194,825)  $243,531

Since they already owe $118,548, the most they could borrow with a second loan is

$243,531  $118,548  $124,983.

If they borrow the maximum, they will owe a total of $184,084 and their home equity would
be reduced to

$194,825  $243,531  $48,706.

This loan would certainly allow them to borrow quite a bit more, but the idea of owing
nearly $50,000 more on a property than it is worth may not be entirely appealing for obvious
reasons.

Types of Mortgage Loans


The market for mortgages is enormous, and the variety of different types of mortgages avail-
able is likewise immense. It would be an exaggeration to say that mortgages are available with
absolutely any features someone might want—but not as much of an exaggeration as you might
think. Most needs, though, can be met with a mortgage fitting into one of these standard types.
A fixed (or fixed-rate) mortgage has an interest rate that is set at the beginning and never
changes over the entire term of the loan. All of the mortgage examples in Chapter 4 were
fixed-rate loans. The most common term for a fixed rate loan is 30 years, with 15 years
being the next most common. Terms of 10 and 20 years are also not unusual, and in recent
years terms as long as 40 years have become available. However, fixed-rate loans can be
found with just about any reasonable term (and, depending on your point of view, per-
haps some unreasonable ones as well). Because the interest rate on a fixed-rate loan never
changes, neither does the payment. While you usually can pay extra to save on interest and
reduce the time required to pay off the loan (as discussed in Chapter 4), doing so does not
normally allow you to lower your payment in later months.
If mortgage rates drop during the term of the loan, a borrower can often take advantage of
this by refinancing (as discussed in Chapter 4). However, if mortgage rates go up, the lender
cannot raise a fixed rate. This system obviously gives an advantage to the borrower. The rates
on shorter-term fixed mortgages will often be lower than on longer terms, largely because with
a longer term the risk that interest rates will work against the lender at some point is greater.
An adjustable-rate mortgage (or ARM) is a more complicated type of loan. An
adjustable-rate loan will usually have some initial period of time for which the rate is
fixed. After that, the rate can change, and when the rate changes the payment may change
as well (we say that the loan is reamortized at that point). The loan’s provisions should
specify exactly when the rate can be adjusted (often once a year), and usually set the new
rate according to some independent benchmark. Common benchmarks used for this are the
average yield on U.S. Treasury bonds or the London Interbank Offered Rate (the LIBOR).
Using an index ensures that while the lender can raise the rate, it cannot do so arbitrarily.
Changes in the rate must be in line with prevailing interest rates in the market.

10.2 Mortgages 435
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