The Mathematics of Money

(Darren Dugan) #1

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


10.1 Credit Cards 449


  1. Warren and Stella bought a house for $154,035. They made an $8,000 down payment. Their lender required them to
    pay PMI on the loan. Four years later, their mortgage balance has been reduced to $139,035, and the market value of
    their house had grown to $163,500. (a) Find their equity today. (b) Is their equity high enough that they will be able to
    eliminate their PMI?

  2. Karam owes $172,835.19 on his mortgage. His house is worth $279,000. How much equity does he have in the
    house?

  3. Bruce is taking out a 25-year fi xed-rate mortgage for $119,500. He has a choice of a 7.9% rate with no points or a
    7.5% rate with 1¼ points. What is the payback period for the points on this loan? If Bruce expects to sell this house in
    5 years, is it fi nancially worthwhile for him to pay the points? Explain.

  4. Felipe’s house is worth $183,500 and he owes $162,104. His bank offers him a home equity loan with a maximum LTV
    of 95%. How much could Felipe borrow?


I. Additional Exercise


  1. Five years ago, Kris bought a house for $135,000. He made a 5% down payment, and fi nanced the rest with a 30-year
    fi xed-rate loan at 6.96%. He has made all of his monthly payments exactly as scheduled. In the past 5 years, the real
    estate market in his town has been hot, and the value of his house has risen at a 5.5% annual rate. How much equity
    does Kris have in the house today?


10.3 Installment Plans


Many major purchases are made with the aid of some sort of borrowing. The reasons for
this are obvious; many buyers do not always have the ability to pay for expensive consumer
goods they want or need in cash. For consumers who want to buy, and merchants who want
to sell, goods such as refrigerators, computers, big screen TVs, and pianos, “a few dollars
down and easy monthly payments” can make the expense of these purchases seem much
easier to swallow.
Any purchase made with the assistance of borrowing is said to be on credit. We have
already explored a number of options for credit purchases. For large purchases like houses
or cars, a secured loan (a mortgage or auto loan) is the most common approach.
For other, smaller scale but still expensive, items, the purchase may often be made
with a credit card. Installment plans present another option that we will explore in this
section.
A fixed-payment installment plan is essentially a loan, usually made to allow the pur-
chase of a particular item, repaid by making a set series of payments. These plans may
be offered by a merchant (though usually the merchant would arrange the actual financ-
ing through an outside finance company) or through a traditional bank. These installment
plans normally (though not always) require some down payment to be made, and then the
remaining balance is assessed a finance charge (also known as the carrying charge), and
the total of the remaining balance and its carrying charge is divided evenly among the
number of payments. These plans are typically fairly short term arrangements, and often
carry very high interest rates.

10.3 Installment Plans 449
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