Introduction to Finance

TA B L E 9 . 1
Future Value Interest Factor (FVIF) of $1
Year
5%
6%
7%
8%
9%
10%
1
1.050
1.060
1.070
1.080
1.090
1.100
2
1.102
1.124
1.145
1.166
1.188
1.210
3
1.158
1.191
1.225
1.260
1.295
1.331
4
1.216
1.262
1.311
1.360
1.412
1.464
5
1.276
1.338
1.403
1.469
1.539
1.611
6
1.340
1.419
1.501
1.587
1.677
1.772
7
1.407
1.504
1.606
1.714
1.828
1.949
8
1.477
1.594
1.718
1.851
1.993
2.144
9
1.551
1.689
1.838
1.999
2.172
2.358
10
1.629
1.791
1.967
2.159
2.367
2.594
0
1
2
3
4
5
6
7
8
9
10
Years
Compound Annual
Interest Rate
Future Value (of $1)
$3.00
2.75
2.50
2.25
2.00
1.75
1.50
1.25
1.00
10%
5%
0%
($2.59)
($1.63)
($1.00)
FIGURE 9.1
 Future Value, 
Interest Rate, and Time Period 
Relationships

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9.3 Discounting to Determine Present Values
225
Inflation or Purchasing Power Implications
The compounding process described in the preceding section does not say anything about the 
purchasing power of the initial $1 investment at some point in the future. As seen, $1 growing 
at a 10 percent interest rate would be worth $2.59 (rounded) at the end of ten years. With zero 
infl ation
, you could purchase $2.59 of the same quality of goods after ten years relative to 
what you could purchase now. However, if the stated, or 
nominal
, interest rate is 10 percent 
and the infl ation rate is 5 percent, then in terms of increased purchasing power, the “net” or 
diff erential compounding rate would be 5 percent (10 percent – 5 percent) and $1 would have 
an infl ation-adjusted value of $1.63 after ten years. This translates into an increased purchas-
ing power of $0.63 ($1.63 – $1.00).
Also note that if the compound infl ation rate is equal to the compound interest rate, the 
purchasing power would not change. For example, if in Figure 9.1 both the infl ation and 
interest rates were 5 percent, the purchasing power of $1 would remain the same over time. 
Thus, to make this concept operational, subtract the expected infl ation rate from the stated 
interest rate and compound the remaining (diff erential) interest rate to determine the change in 
purchasing power over a stated time period. For example, if the interest rate is 10 percent and 
the infl ation rate is 3 percent, the savings or investment should be compounded at a diff erential 
7 percent rate. Turning to Table 9.1, we see that $1 invested at a 7 percent interest rate for ten 
years would grow to $1.967 ($1.97 rounded) in terms of purchasing power. Of course, the 
actual dollar value would be $2.594 ($2.59 rounded).
GLOBAL
Financial contracts (e.g., savings deposits and bank loans) in countries that have exper-
ienced high and volatile infl ation rates sometimes have been linked to a consumer price or similar 
infl ation index. Such actions are designed to reduce the exposure to infl ation risk for both savers 
and lenders. Since the interest rate they receive on their savings deposits will vary with the rate of 
infl ation, savers receive purchasing power protection. As infl ation rises, so will the rate of interest 
individuals receive on their savings deposits such that purchasing power will be maintained.
Bank lenders are similarly protected against changing infl ation rates, since the rates they 
charge on their loans will also vary with changes in infl ation rates. At least in theory, banks 
will be able to maintain a profi t spread between the interest rates they pay to savers and the 
higher interest rates they lend at to borrowers, because infl ation aff ects both fi nancial con-
tracts. Of course, if the borrowers are business fi rms, they need to be able to pass on higher 
prices for their products and services to consumers to be able to maintain profi t margins when 
interest rates are rising along with increases in infl ation.
Infl ation in the United States has averaged about 2 percent annually during the fi rst part 
of the twenty-fi rst century. However, some economists and others have expressed concern 
that the Fed’s emphasis since late-2008 on near zero federal funds interest rate targets and its 
QE1, QE2, and QE3 quantitative easing eff orts will result in much higher infl ation rates in the 
future. The Fed responded in late-2015 with its fi rst of what are likely to be several increases 
in the federal funds target interest rates to combat possible increases in infl ation.