The Mathematics of Money

444 Chapter 10 Consumer Mathematics

Subtracting to fi nd the difference, we can see that, over 30 years, they would save

$37,483.20.

While the $3,117.34 up front doesn’t sound particularly appealing, saving $37,483.20 cer-

tainly does. This figure can be deceptive though, because it is based on the assumption that

Drew and Joanne will actually keep this loan for the full 30 years. If they decide to move,

if interest rates drop and they seize the opportunity to refinance, or if they pay extra on the

loan to kill it off sooner, they will not see the full savings. In fact, it is rare that a 30-year

loan actually stays around for a full 30 years, because one of those events is very likely to

happen over the course of 30 years.

One tool that is sometimes used to assess whether or not an up-front expense is worth it

or not is the payback period. To calculate the payback period, we simply look at how much

Drew and Joanne would save on their monthly payment, and determine how many months

it would take for those savings to add up to the cost of the points.

Example 10.2.11 Find the payback period for the decision to pay points in the

previous example.

If they pay the points, their monthly payment will be $871.88  $767.76 
 $104.12. Then

$3,117.34/$104.12 
 29.94 or just about 30 months.

So we conclude it will take about 30 months for Drew and Joanne to recoup their investment

in the points.

Payback periods are a crude tool, and don’t take everything into account perfectly (they

ignore the time value of money for example), but they do provide a helpful way of look-

ing at the points decision. Until 30 months have passed, the accumulated savings from

the lower payment does not add up to the cost of the points. But from that point on, the

savings from the points will exceed their cost. Knowing how long it will take for them to

recoup their investment in those points may help them to evaluate whether or not they are

worth the expense. (Payback periods as a tool for financial decision making are discussed

in greater depth in Chapter 14.)

EXERCISES 10.2

A. The Language of Mortgages

1. Howard and Lita own a house worth $128,000. They have a mortgage on the house, with an outstanding balance of
   $89,537. How much home equity do they have?


2. A corporation owns the offi ce building that houses its headquarters. The value of the property is $1,535,000. The
   balance on the mortgage on the property is $915,888. Find the corporation’s equity in the building.


3. Sally owes $87,309 on the mortgage on a condo that she owns, which is worth $115,000. She wants to take out a
   home equity loan. The bank loan offi cer tells her that the maximum loan to value percent is 90%. How much could
   Sally borrow?


4. Bill owns an apartment building worth $450,000. He has a mortgage on the property with a balance of $338,919. If he
   takes out the largest home equity loan he can from a bank that requires him to have a minimum of 8% in equity in the
   property, how much can he borrow? If he does this, what will his equity be?