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164 PART 2 Important Financial Concepts
FOCUS ON PRACTICE Time Is on Your Side
For many years, the 30-year fixedrate
mortgage was the traditional
choice of home buyers. In recent
years, however, more homeowners
are choosing fixed-rate mortgages
with a 15-year term when
they buy a new home or refinance
their current residence. They are
often pleasantly surprised to discover
that they can pay off the
loan in half the time with a monthly
payment that is only about 25 percent
higher. Not only will they own
the home free and clear sooner,
but they pay considerably less interest
over the life of the loan.
For example, assume you
need a $200,000 mortgage and can
borrow at fixed rates. The shorter
loan would carry a lower rate (because
it presents less risk for the
lender). The accompanying table
shows how the two mortgages
compare: The extra $431 a month,
or a total of $77,580, saves $157,765
in interest payments over the life
of the loan, for net savings of
$80,185!
WWW
In Practice
Monthly principal Total interest paid
Term Rate and interest over the term of the loan
15 years 6.50% $1,742 $113,625
30 years 6.85% $1,311 $271,390
Why isn’t everyone rushing to
take out a shorter mortgage? Many
homeowners either can’t afford
the higher monthly payment or
would rather have the extra spending
money now. Others hope to do
even better by investing the difference
themselves. Suppose you invested
$431 each month in a mutual
fund with an average annual
return of 7 percent. At the end of
15 years, your $77,580 investment
would have grown to $136,611, or
$59,031 more than you contributed!
However, many people lack the
self-discipline to save rather than
spend that money. For them, the
15-year mortgage represents
forced savings.
Yet another option is to make
additional principal payments
whenever possible. This shortens
the life of the loan without committing
you to the higher payments. By
paying just $100 more each month,
you can shorten the life of a 30year
mortgage to 241/4 years, with
attendant interest savings.
Sources: Daniela Deane, “Adding Up Pros,
Cons of 15-Year Loans,” Washington Post
(October 13, 2001), p. H7; Henry Savage, “Is
15-Year Loan Right for You?” Washington
Times (June 22, 2001), p. F22; Carlos Tejada,
“Sweet Fifteen: Shorter Mortgages Are Gaining
Support,” Wall Street Journal (September
17, 1998), p. C1; Ann Tergesen, “It’s Time
to Refinance . . . Again,” Business Week
(November 2, 1998), pp. 134–135.
Table Use The first step in finding the interest or growth rate is to divide the
amount received in the earliest year (PV) by the amount received in the latest year
(FV n). Looking back at Equation 4.12, we see that this results in the present value
interest factor for a single amount for 4 years, PVIF i,4yrs, which is 0.822
($1,250$1,520). The interest rate in Table A–2 associated with the factor closest
to 0.822 for 4 years is the interest or growth rate of Ray’s cash flows. In the
row for year 4 in Table A–2, the factor for 5 percent is 0.823—almost exactly the
0.822 value. Therefore, the interest or growth rate of the given cash flows is
approximately (to the nearest whole percent) 5%. 13
Calculator Use Using the calculator, we treat the earliest value as a present
value, PV, and the latest value as a future value, FV n.(Note: Most calculators
13. To obtain more precise estimates of interest or growth rates, interpolation—a mathematical technique for estimating
unknown intermediate values—can be applied. For information on how to interpolate a more precise answer
in this example, see the book’s home page at www.aw.com/gitman.