The Mathematics of Money

(Darren Dugan) #1

Copyright © 2008, The McGraw-Hill Companies, Inc.


so will also usually require escrow for insurance. Insurance escrow works in essentially the
same way as tax escrow.
One additional expense that may be included with your monthly payment is private
mortgage insurance (usually just referred to as PMI ). PMI is an insurance that protects the
mortgage lender financially in the event that you do not pay and they are forced to foreclose.
At first, this sounds completely unnecessary. Suppose you bought a $150,000 house.
Even if you made a small down payment of $5,000 (just over 3%), the amount borrowed
would be $145,000, less than the house is worth. Even if you never made a single payment,
the lender has the right to foreclose on a house worth more than the amount they are owed.
Why on earth would they need insurance to protect them from this situation?
This is an overly simple way of looking at things though. If the bank has to foreclose on
you, it will incur all sorts of expenses, including:

Legal fees incurred to foreclose
Costs of transferring ownership of the property
Lost interest on its money (its money is tied up in the loan, but you aren’t paying inter-
est on it any more)
Costs of marketing and selling the property
Costs of maintaining the property (someone has to mow the lawn, pay the electric bill,
patch roof leaks, etc.)
Costs for repairs to the property (people about to lose their homes to foreclosure are
often not in the mood to keep the place ship-shape)
Taxes and insurance (both delinquent from what you did not pay as well as the costs
for the time the lender owns the property)

Furthermore, the mortgage lender is in the business of making loans, not owning real estate.
Often, in order to sell the property quickly, it will have to accept a lower price than the
property might command with a seller willing to hold out for the best offer. The “$150,000
house” may sell for quite a bit less, and the costs and expenses of foreclosure may add up
to tens of thousands of dollars. The end result is that the lender will recover a good deal
less than the $145,000 it is owed. All in all, the lender in this situation can be left with a
substantial loss, even though the loan was secured by a house worth more than the amount
owed. The purpose of PMI is to help cover the lender’s losses from this sort of situation.
If your down payment is 20% or more, the lender will not require PMI. In that case, the
gap between the property’s value and the amount owed is wide enough so that the lender’s
risk is minimal, even if it does wind up having to foreclose. Some lenders also offer loans
without PMI with down payments less than 20%, though you may pay for that with a higher
interest rate. When your equity reaches 22% based on the original amortization schedule,
PMI must be removed automatically. You can also apply to have it removed sooner when-
ever your equity reaches 20%, which will usually occur as a result of a combination of the
balance declining from your payments and an increase in the value of the property.

Example 10.2.5 Suppose Ben bought a house for $146,000, taking out a $135,000
mortgage. Three years later, his mortgage balance has declined to $132,833.15 and
the house’s market value has grown to $168,000. Can Ben apply to have his PMI
discontinued?

Ben’s equity is now $168,000  $132,883.15  $35,116.85. This is $35,116.85/$168,000 
20.90% equity, so the answer is yes.

Total Monthly Payment (PITI)


Since escrow and PMI (if required) are additional monthly expenses, looking at the monthly
mortgage payment by itself as your “monthly payment” is a bit misleading. In fact, in most
cases the monthly payment made to the mortgage lender will include all of these costs


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10.2 Mortgages 439
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