How do you account for inflation when comparing dollar amounts over time?

Answer 1

Accounting for inflation over time requires you to take purchasing power into account, thus specific rates of inflation for certain things can differ from the overall inflation of a society.

If inflation is 3% a year, then $1 this year will only be able to purchase 97 cents worth of goods next year.

So if you have a consistent inflation rate of 3% a year, and want to compare the purchasing power of one dollar from 10 years ago to the current day, then for the first year of inflation, one dollar would drop to 97 cents, and then from there to the next year, 97 cents would only buy 97% of what it could buy the previous year.

Due to this, you cannot simply multiply 3% by the number of years to find the total effect of inflation.

So you would go from $1 to 97 cents one year, and then 97 cents to 94.09 cents of purchasing power over the next year. Then from 94.09 cents to 91.2673 cents the next year.

In order to easily calculate this, you could instead simply take the initial amount of money (lets say $1), and multiply it by (1-r)^n. In this, r is the inflation rate, so that 3% would be 0.03, thus 1-0.03 is 0.97. The variable n is the number of years from year 1.

So if you were to take 1 dollar, and place it into the equation with inflation at 3% a year, you'd find that 1 * (0.97^1) = 97 cents, just like we found up above. 1 * (0.97^2) = 94.09 cents, again as found above.

So $100 dollars in the first year, before any inflation has kicked in, would only be worth $21.80 after 50 years of 3% annual inflation.