Copyright © 2008, The McGraw-Hill Companies, Inc.
Topic Key Ideas, Formulas, and Techniques Examples
Finding Loan Payments,
pp. 175–176- Use the present value annuity formula, fi nd the
annuity factor, and then use algebra to fi nd the
payment amount.
Pat and Tracy took out a
30-year, $158,000 mortgage
at 7.2%. How much will
their monthly payment be?
(Example 4.4.8)Finding Total Interest Paid,
pp. 175–176- To fi nd the total interest paid in an annuity,
subtract the present value from the total of the
payments.
Pat and Tracy took out a
30-year, $158,000 mortgage
at 7.2%. How much total
interest will they pay?
(Example 4.4.8)The Present Value of an
Annuity Due, p. 177- The Present Value Annuity Due
Formula: PV PMT a _n (^) | (^) i(1 i)
- The calculation is done the same way as an
ordinary annuity’s, but then multiply by (1 i) at
the end
A lottery jackpot is paid out
as annual $2 million payments
for 26 years. If you choose
instead to receive a lump
sum payment all at once,
how much will you receive,
assuming a 6% interest rate?
(Example 4.4.11)
Amortization Tables, p. 183 • An amortization table shows payment by
payment the amount of interest, the amount of
principal, and remaining balance on a loan.- The amount to interest is calculated by using
the simple interest formula. - The amount to principal is the difference
between the payment and the interest amount. - The remaining balance is the previous period’s
balance, less the amount paid to principal.
Pat and Tracy took out a
30 year, $158,000 mortgage
at 7.2%. Create an
amortization table for their
fi rst twelve monthly payments.
(Example 4.5.1)The Remaining Balance of a
Loan, p. 186- To fi nd the remaining balance on an amortized
loan, calculate the present value of the remaining
payments.
Assuming that they make all
their payments as scheduled,
how much will Pat and Tracy
owe on their mortgage after
10 years? (Example 4.5.3)Consolidation and
Refi nancing, p. 187- A loan may be paid off by borrowing the amount
needed to do so with a new loan. - Refi nancing is replacing a single loan with a
new one. Consolidation is replacing several
loans with a single new loan. - Determine the amount owed on each loan, and
then use the result as the present value of the
new loan.
Kwame has 12 years
remaining on a business loan
at 15%. His payments are
$2,531. What would his new
payment be if he refi nances
with a 12-year loan at 8%?
(Example 4.5.4)The Chronological Approach
to Future Values with Irregular
Payments (Optional),
pp. 192–193- The future value of a stream of payments that is
not an annuity can be calculated by building the
future value chronologically.
For 2 years, I deposited $175
monthly. For the next 3 years
there were no payments
made. If my account earned
3.6%, what was my future
value? (Example 4.6.1)The Bucket Approach to
Future Values with Irregular
Payments (Optional), p. 197- The future value of a stream of payments that is
not an annuity can be calculated by imagining
the payments broken up into separate accounts
(“buckets”).
Kevin deposited $1,000 each
year into an account earning
5% for 10 years. In the third
year, though, he deposited
$5,000 instead of $1,000.
Find his future value.
(Example 4.7.2)Chapter 4 Summary 203