Copyright © 2008, The McGraw-Hill Companies, Inc.
You may want to review the material from Section 4.4 covering present values of annuities.
In particular, you should make sure that you know how to calculate present value annuity
factors, as we will be using them quite a bit in this section. You are encouraged to work
through the calculations of the example above to make sure that you can find the annuity
factor correctly.Calculating Monthly Mortgage Payments (Adjustable-Rate Loans)
Payments for adjustable-rate loans are calculated in the same way as those for fixed rate
loans. The difference is that periodically the payment will be recalculated for the remaining
loan balance, term, and new interest rate.Example 10.2.4 Suppose that instead of being a 30-year fi xed loan, the mortgage
in the prior example was a 5/30 adjustable rate loan, with a 7.2% interest rate. Find
Chantal’s monthly payment.Her mortgage payment would be calculated in exactly the same way as in Example 10.2.3,
since the term is still 30 years and the interest rate is still 7.2%. The difference between the
two examples is that with the fi xed-rate loan her payment will remain the same for the entire
30-year term. With the 5/30 ARM, her payment will be $963.88 for the fi rst 5 years. After
that time, her payment will most likely change, depending on the interest rate at the remain-
ing balance owed at that time (it may either increase or decrease).APRs and Mortgage Loans
Mortgage lenders are required by law to disclose an APR for their mortgage loans. The
intended purpose of this APR is the same as the APY for an interest-bearing account (as
discussed in Chapter 3): to allow an “apples-to-apples” comparison between different loan
offerings. One lender may offer a 7.25% rate for a 30-year fixed loan, while another may
offer a 7% for a similar loan, but make up for this lower rate with much higher fees and other
charges. The APR is intended to take into account many of the extra fees and expenses.
The calculation of the APR is a highly complicated matter. There is little need for us
to get involved in the calculation of APRs here. As a consumer, though, it is important to
recognize certain things about mortgage APRs:APRs are meant to help make an overall comparison between similar mortgage prod-
ucts offered by different lenders by taking into account both interest and some other
expenses that may be charged
APRs do not necessarily include every expense that might be charged
APRs cannot reasonably be used to compare different mortgage products. A fi xed-rate
loan is by its nature signifi cantly different from an ARM, and so simply comparing APRs
between the two products overlooks the differences in the nature of the products
APRs for adjustable rate loans must be calculated on the basis of assumptions about where
the rates will be adjusted in the future, even though this cannot be known in advanceAnd, most importantly for our purposes:In calculating the monthly payment, do not use the APR! The APR is not the actual inter-
est rate used to determine the payment, nor is it used in a loan’s amortization schedule.Some Additional Monthly Expenses
In Chapter 4, we saw how to find the monthly payment on a fixed mortgage loan. The
amount borrowed is the present value of an annuity. However, there are other regular
expenses of owning a home beyond just the mortgage payment.
Real property taxes (sometimes called real estate taxes or simply property taxes) are
taxes that you must pay on the basis of the value of real estate that you own. They may
be levied by state, county, or local governments and/or school districts. Real property tax10.2 Mortgages 437