The Mathematics of Money

(Darren Dugan) #1

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


Topic Key Ideas, Formulas, and Techniques Examples


Projections with
Infl ation, p. 323


  • Infl ation has historically averaged 3 to 3.5%
    over the long term in the United States

  • Projections about infl ation use the same
    mathematical formula as compound interest.


A lawnmower costs $189.95
today and you expect prices
to rise at a 4% effective rate in
the future. If your assumption
is correct, predict the mower’s
price 20 years from now.
(Example 7.3.1)

Retirement Projections in
To day’s Dollars, p. 324


  • Long-term fi nancial projections often overlook
    the impact of infl ation

  • This may be addressed by doing calculations in
    today’s dollars.

  • The real rate of return from an investment is
    found by subtracting the infl ation rate


Working entirely in today’s
dollars, what amount would
you need to deposit each
week to reach $1,000,000
in 40 years, assuming your
account earns 9.1% and
infl ation averages 3.5%?
(Example 7.3.3)

Annuities Whose Payments
Change at a Rate Different
from Infl ation, p. 326


  • Calculations in today’s dollars require the
    payments to change at the same rate as
    infl ation.

  • If payments change at a different rate,
    spreadsheets are required to work out
    projections and other calculations.


What amount would you need
to deposit each week to reach
the equivalent of $1,000,000
worth of today’s dollars,
assuming your account earns
9.1%, infl ation averages
3.5%, and your payments
increase at a 5% annual rate?
(Example 7.3.4)

Chapter 7 Summary 331
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