EXAMPLE 13 Deflated Dollars

Suppose that there is 25% annual inflation from mid-2015 through mid-2019. What would be the value of a dollar in mid-2019 in constant mid-2015 dollars? The inflation figure is unrealistic (we hope!), but it makes the calculations easy so that you can focus on the ideas.

We have . This—not 25%—is the negative interest rate, the rate at which the dollar is losing purchasing power. We have years, so the purchasing power of $1 four years from mid-2015, in terms of 2015 dollars, would be

For a more realistic rate of 3% annual inflation, we would have and negative interest rate . In 2019, the purchasing power of $1 would be

in 2015 dollars. Notice that “losing” 3% to inflation each year for 4 years amounts to losing almost—but not quite as much as—a total of . (This is just as with the previous inflation rate, where losing 25% per year for 4 years doesn’t completely reduce the value to 0.)