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Module 2

Purchasing power over time

A dollar kept in a drawer never changes its number, yet it steadily buys less. In this investigation you will predict, model, and measure how much less.

1Commit to a prediction

Suppose prices across the economy rise by 3 percent each year. You place $100 in a drawer today and open it in 30 years. The bill still reads $100, but how much of today's goods will it buy?

Enter your best estimate in today's dollars before you run any calculation. A recorded prediction makes the result more informative, because it reveals where your intuition is accurate and where it is not.

2Build the model

Each year, prices are multiplied by (1 + i), where i is the annual inflation rate. A fixed sum of money therefore buys 1 / (1 + i) as much as it did the year before. After t years, its value in today's dollars is P / (1 + i)t.

Adjust the inputs, then run the model. The dashed line shows a 2 percent reference rate, the inflation target that the U.S. Federal Reserve, the European Central Bank, and the Bank of England each use.

Loading the Python engine. This takes several seconds on the first visit.

Value in today's dollars
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Purchasing power lost
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Years until value halves
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Rule of 72 estimate
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3Reconcile the model with your prediction

Lock in a prediction in Step 1, then run the model with 3 percent over 30 years to compare.

Why do most people overestimate the remaining value?

Intuition tends to treat inflation as a fixed amount subtracted each year, which is a linear process. Inflation instead compounds, because each year's price increase applies to prices that have already risen. Compounding is gentle at first and severe over long periods, so short-horizon experience gives a misleading sense of the long-horizon result.

How good is the Rule of 72?

The Rule of 72 estimates the halving time as 72 divided by the percentage rate. Compare it with the exact value in Step 2 at several rates. The approximation is close for rates between about 4 and 12 percent and drifts at very low and very high rates. Consider why a shortcut designed for mental arithmetic would favor a number such as 72, which divides evenly by 2, 3, 4, 6, 8, 9, and 12.

Question to carry forward. If money reliably loses purchasing power, what does a person need to do with savings simply to keep pace, and who in the economy benefits when prices rise? Module 3 examines where new money comes from and who receives it first.

4Inspect the code

Nothing on this page is hidden. The Python below is the exact code that produced your results, running in your browser through Pyodide.

Show the Python model 

      

    


    
Related reading. A short history of currency debasement traces this pattern from ancient Rome to the modern dollar.


    

      Previous module, What is money?
      Next module, Central banks and the money supply