Copyright © 2008, The McGraw-Hill Companies, Inc.
b. Not only do shorter terms save you money by paying off the loan more quickly, they often (though not always) offer
a lower interest rate. How much total interest would Kathy have saved if instead of her 30-year loan she had gone
with a 15-year loan at a 5.92% interest rate?- In Exercises 2 to 5 we considered an abbreviated table of annuity factors used by a real estate agent to be able to
quickly calculate mortgage payments. To fi nd the amount to be borrowed based on a payment, you needed to multiply
by these annuity factors; however, to fi nd the payment based on a loan amount, you need to divide.
Sometimes an alternative to these tables is used, which, instead of giving the annuity factor, gives the monthly payment
per $1,000 borrowed. This is sometimes preferred, since if we know this we do not need to divide.
Suppose that our real estate agent Jeff instead had this table:
MONTHLY PAYMENT PER $1,000 BORROWED
INTEREST RATE
Years 7.00% 7.50% 8.00% 8.50% 9.00%
15 $8.99 $9.27 $9.56 $9.85 $10.14
30 $6.65 $6.99 $7.34 $7.69 $8.05Rework Exercises 4 to 5 using this table. Do your answers match?- Rework Exercises 2 and 3, using the table from Exercise 37.
- Create a “payment per $1,000 borrowed” table like the one from Exercise 37, this time for a car salesman who wants
to be able to fi nd monthly payments at interest rates of 6%, 7%, 8%, and 9%, and terms of 3, 4, and 5 years. - As the result of litigation against the tobacco industry, Conesus County received a large judgment, payable as an
annuity over 20 years. Rather than take its payments over time, the county decided to “sell” these payments to
a fi nance company in exchange for a lump sum. Company A offered to give the county the present value calculated
at a 9% interest rate. Company B offered a 10% rate. Which company offered the better deal? Why?
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4.5 Amortization Tables
There were some surprises in Section 4.4. In Examples 4.4.8 and 4.4.9, we compared a 30-year
mortgage to a 15-year mortgage, and found that, despite the commonsense expectation that
halving the time would require doubling the payments, the 15 year loan’s payments were not
anywhere near twice the 30 year’s. We attributed the difference to the shorter term’s allowing
for less interest, which generally makes sense, but it is a bit unsatisfying to have to leave it
at that. Unfortunately, our annuity factor formulas allow us only to calculate payments from4.5 Amortization Tables 181