Principles of Managerial Finance

184 PART 2 Important Financial Concepts

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

In Practice

For many years, the 30-year fixed-

rate mortgage was the traditional

choice of home buyers. In recent

years, however, more homeown-

ers are choosing fixed-rate mort-

gages with a 15-year term when

they buy a new home or refinance

their current residence. They are

often pleasantly surprised to dis-

cover that they can pay off the

loan in half the time with a monthly

payment that is only about 25 per-

cent higher. Not only will they own

the home free and clear sooner,

but they pay considerably less in-

terest 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 mort-

gages 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!

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 spend-

ing money now. Others hope to do

even better by investing the differ-

ence themselves. Suppose you in-

vested $431 each month in a mu-

tual 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 commit-

ting you to the higher payments. By

paying just $100 more each month,

you can shorten the life of a 30-

year mortgage to 24^1 / 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 Gain-

ing Support,”Wall Street Journal (Septem-

ber 17, 1998), p. C1; Ann Tergesen, “It’s Time

to Refinance... Again,” Business Week

(November 2, 1998), pp. 134–135.

FOCUS ONPRACTICE Time Is on Your Side

To find the equal annual payment required to pay off, or amortize, the loan,

PVAn, over a certain number of years at a specified interest rate, we need to solve

Equation 4.26 for PMT.Isolating PMT on the left side of the equation gives us

PMT (4.27)

Once this is done, we have only to substitute the known values into the righthand

side of the equation to find the annual payment required.

EXAMPLE As just stated, you want to determine the equal annual end-of-year payments nec-

essary to amortize fully a $6,000, 10% loan over 4 years.

Table Use Table A–4 indicates that the present value interest factor for an

annuity corresponding to 10% and 4 years (PVIFA10%,4yrs) is 3.170. Substituting

PVA 4 $6,000 and PVIFA10%,4yrs3.170 into Equation 4.27 and solving for

PMTyield an annual loan payment of $1,892.74. Thus to repay the interest and

principal on a $6,000, 10%, 4-year loan, equal annual end-of-year payments of

$1,892.74 are necessary.

PVAn



PVIFAi,n