The Mathematics of Money

(Darren Dugan) #1

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



  1. Liankung owns a house worth $218,500. He has two mortgages on the property. The balance on the fi rst mortgage is
    $132,890 and on the second the balance is $52,675. A fi nance company offers him the opportunity to borrow more
    against the house, allowing a maximum loan to value of 115%. If he takes out the largest loan the bank will allow, how
    much can he borrow? What would his equity be then?


B. Calculating Monthly Mortgage Payments

Note that the problems in this section require calculation of the payment on the mortgage loan itself only.


  1. Find the monthly payment on a 30-year fi xed mortgage loan of $108,525 if the interest rate is 6¾%.

  2. Find the initial monthly payment on a 3/20 ARM of $178,802 if the interest rate is 5.35%. How long will it be before the
    interest rate (and thus the payment) can change?


C. Escrow Accounts


  1. How much will my monthly escrow payment be if my property taxes are expected to be $2,895 annually and my
    homeowners’ insurance premium is $745 per year?

  2. Find the monthly escrow payment for someone whose annual property taxes are $3,900 and homeowners’ insurance
    premium is $663.

  3. Jack and Tania’s homeowners’ insurance premium is $1,252, and their property taxes are $5,254. How much will their
    monthly escrow payment be?


D. Total Monthly Payment (PITI)


  1. Mike’s monthly mortgage payment is $675.13. His property taxes are $1,392 and his homeowners’ insurance premium
    is $885. He also pays $48.17 a month for PMI. Find his total monthly PITI payment.

  2. Suppose that for the property in Exercise 6 the property taxes are $1,725 and homeowners’ insurance costs $607. PMI
    of $57.25 is also required. Find the total monthly PITI.

  3. Aaron and Cienna are considering buying a house for $175,000. They would make a $10,000 down payment, and
    borrow the rest with a 30-year fi xed mortgage at 7.45%. Annual property taxes would be $5,700, and homeowners’
    insurance would be $935. They would also need to pay $84.00 monthly for PMI. What would their total monthly
    payment (PITI) be?

  4. Russ is contemplating making an investment by buying a rental property. The cost of the building would be $399,000,
    and he can afford to make a 20% down payment. He plans to fi nance the rest with a 25-year mortgage at 6.98%.
    Annual property taxes are $10,384 and insurance would cost him $2,850 per year. What will his monthly payment be?


Exercises 10.2 445
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