The Mathematics of Money

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

This is actually close to the target future value, but a bit short. Trying different initial payments,

through trial and error we fi nd that the closest we can get to our target is by using an initial

payment of $106.35 per week.

This problem could also be done in today’s dollars. In that case, if we assume a 3.5% inflation

rate, we would have the payments increasing by 5% – 3.5% 
 1.5% per year, we would

use a $1,000,000 future value, and would use a growth rate of 5.6%. It is equally reason-

able to do the problem either way; what matters, though, is that, when you do one of these

problems, you do not mix up today’s dollars with actual dollars, since that inconsistency will

lead to unreliable results. Whichever approach you take, always make sure to be consistent!

If you are working a given problem in today’s dollars, consistently use today’s dollars and

be clear about that fact when interpreting your answer. If you are working in actual dollars,

consistently use actual dollars and be clear about that fact when interpreting your answer.

Exercises 7.3 327

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

A. Projecting Future Dollar Amounts with Infl ation

1. Suppose that housing prices rise at a 2.75% annual rate for the next 20 years. Project the future price of a house that
   sells for $183,500 today.


2. Suppose that the rate of infl ation averages 3.75% in the future. Garret wants to have an investment account worth the
   equivalent of $500,000 in today’s dollars in 40 years. What is the actual dollar amount of his goal?


3. Suppose that food prices rise at an average 4.5% rate for the next 15 years. Based on this rate, predict the price of a
   box of cereal that currently costs $3.49.


4. In 2005, Gena was quoted a price of $24,583 for a large array of solar panels for her home. An industry expert was
   predicting that prices for solar arrays would drop at a roughly 10% annual rate for the next 10 years. If this prediction is
   correct, how much would this array cost in 2015?

B. Financial Projections with Infl ation

5. Suppose that I believe that my investment portfolio can earn 8.5%. If the infl ation rate averages 3.5%, what is my real
   rate of return?


6. In Section 6.4 we presented a table of average annual historical rates of return for different asset classes. These rates
   were not adjusted for infl ation. Fill in the table below to include a column for the real rate of return, assuming infl ation
   runs at a 3.5% average rate.

Asset Class Degree of Risk

Historical AverageRate

of Return

Historical Average Real

Rate of Return

Cash Minimal 2–5%

Fixed Income Moderate 4–7%

Equities High 8–12%

EXERCISES 7.3