Fermi estimate: size the outstanding stock of US one-dollar notes

Quick Overview

A Fermi estimation interview question asking how many dollar bills are circulating in the United States. It tests defining the denomination and what counts as in circulation, estimating a stock of notes rather than a flow of spending, structuring labeled assumptions about where cash sits, and sanity-checking the result.

Fermi estimate: size the outstanding stock of US one-dollar notes

Company: Google

Role: Product Manager

Category: Product / Decision Making

Difficulty: medium

Interview Round: Other

Estimate how many US dollar bills are circulating right now. Explain how you structure the estimate, label each assumption, show the arithmetic and finish with a single number. ```hint Stock, not flow Money spent over a year is not the same thing as the number of notes that exist at one moment. Think about where the notes are sitting today. ``` ### Clarifying Questions - Does "dollar bills" mean only \$1 notes, or every denomination of US paper currency? - Does cash held in bank and credit union vaults count, or only cash in the hands of people and businesses? - Do notes held outside the United States count? - Should notes that were lost or put away years ago, but never returned to be destroyed, be included? ### What a Strong Answer Covers - A clear scope: which denomination, and what counts as "in circulation". - An approach that counts a stock of notes rather than a year of spending, with buckets that cover where notes actually sit. - Labeled, rounded assumptions and correct arithmetic across millions and billions. - A sanity check from a second angle and the assumptions that move the answer most. ### Follow-up Questions - How would your approach change if the interviewer meant all denominations? - Card and phone payments keep growing. Would you expect the count to fall, and why might it not? - If you could look up one statistic to tighten the estimate, which would you choose?

Overview: A Fermi estimation interview question asking how many dollar bills are circulating in the United States. It tests defining the denomination and what counts as in circulation, estimating a stock of notes rather than a flow of spending, structuring labeled assumptions about where cash sits, and sanity-checking the result.

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Google
Jun 17, 2024
mediumProduct ManagerOtherProduct / Decision Making
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Estimate how many US dollar bills are circulating right now. Explain how you structure the estimate, label each assumption, show the arithmetic and finish with a single number.

Clarifying Questions Guidance

  • Does "dollar bills" mean only $1 notes, or every denomination of US paper currency?
  • Does cash held in bank and credit union vaults count, or only cash in the hands of people and businesses?
  • Do notes held outside the United States count?
  • Should notes that were lost or put away years ago, but never returned to be destroyed, be included?

What a Strong Answer Covers Guidance

  • A clear scope: which denomination, and what counts as "in circulation".
  • An approach that counts a stock of notes rather than a year of spending, with buckets that cover where notes actually sit.
  • Labeled, rounded assumptions and correct arithmetic across millions and billions.
  • A sanity check from a second angle and the assumptions that move the answer most.

Follow-up Questions Guidance

  • How would your approach change if the interviewer meant all denominations?
  • Card and phone payments keep growing. Would you expect the count to fall, and why might it not?
  • If you could look up one statistic to tighten the estimate, which would you choose?