436 Chapter 10 Consumer Mathematics
There will also normally be a cap on how much the rate can change at a time (such as
not more than 2% at each adjustment), and an overall limit on the highest the rate can go
under any circumstances. These limits are referred to as caps.
The term of an adjustable rate loan will specify both the length of the initial fixed period
and the overall term of the loan. A 7/30 adjustable rate, for example, would be a loan that
has a rate that is fixed for the first 7 years, and then varies for the next 23 years.
Adjustable-rate loans often will carry better interest rates up front than fixed-rate loans,
since if interest rates rise, the lender is not at nearly the same risk of being stuck with a
loan at an uncompetitive rate. For the same reason, the shorter the fixed period, the better
the initial rate is likely to be.
In recent years, there has been an increase in the availability of some very flexible
mortgage products. One example of this is interest-only mortgages. With such loans, the
borrower may only be obligated to pay enough to cover the interest on the loan each month,
and may not have to pay anything against the principal. This option to pay only the interest
may be permitted for a short introductory period, or for a more extended period of time.
While these loans are attractive because of their flexibility, they of course pose the danger
that, if nothing is paid against the principal, the process of amortization never begins, and
no progress is made toward paying off the loan.
Occasionally loans may be even be offered that allow payments that are even less than
the amount of interest for a period of time, in which case instead of declining, the amount
owed actually grows. This situation is sometimes called negative amortization. These
sorts of loans can be attractive because of their flexibility and because they can make pay-
ments on a large loan appear more digestible, but they can also be dangerous. As we have
seen in our prior work, if no progress is made toward paying off the balance, the interest
costs over time can add up to staggering amounts. These sorts of loans also can be danger-
ous in that keeping the initial payments low can tempt a borrower to take on more overall
debt than he can really handle in the long term. In some cases the interest may not be
allowed to compound, meaning that while interest accumulates on the balance, there is no
“interest on interest” building up. The mathematics behind those sorts of loans is therefore
quite a bit trickier than on standard sorts of loans, which assume that interest is paid on the
entire balance each month.
It is generally believed that home ownership is a good thing both for individual families
and for society as a whole. To make it easier for families to own their own homes, and
to encourage them to do so, there are many government-sponsored programs, at both the
state and federal levels (and sometimes even the local government level). Two of the more
common programs are the Federal Housing Administration (FHA), and programs offered
through the Department of Veterans Affairs (VA). These programs may offer help in pay-
ing some of the costs of obtaining a loan, may offer especially low interest rates, or may
offer loans to people who would not otherwise qualify for a mortgage loan. Such programs
usually have specific criteria for who can qualify (such as only people with incomes below
a set level, or those who have served in the military, and so on).
A loan for which the borrower qualified without any such programs is called a conven-
tional loan.Calculating Monthly Mortgage Payments (Fixed Loans)
We discussed how to find monthly mortgage payments in Chapter 4. The following example
is intended to refresh your memory about these calculations.Example 10.2.3 Chantal took out a $142,000 mortgage with a 30-year, fi xed-rate
loan at 7.2%. Find her monthly mortgage payment.PV PMT a _n (^) |i
$142,000 PMT a ___ 360 | (^) 0.006
$142,000 PMT(147.321356802)
PMT $963.88