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Money Supply, Monetary Base & Reserve-Ratio Model

Relate currency, deposits and bank reserves to a simplified monetary base, money supply and their ratio.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

With deposits of 100 million, a reserve-to-deposit ratio of 10 percent and public currency of 20 million, reserves are 10 million, the base is 30 million and money supply is 120 million. The modeled multiplier is 4.

Reserves = reserve ratio Ă— deposits; base = currency + reserves; money supply = currency + deposits; multiplier = money supply/base

Worked example

Enter these known values and leave the other values blank.

Deposits included in this model
100 USD · million
Reserve-to-deposit ratio
10 %
Currency held by the public
20 USD · million
Bank reserves
10 USD · million
Modeled monetary base
30 USD · million
Modeled currency-plus-deposit supply
120 USD · million
Supply divided by monetary base
4

Assumptions and limitations

  • Enter monetary stocks for the same date, currency and definition. The size selector defaults to millions; it can also show billions or trillions. Currency conversions retain the captured reference rates and are not live quotes.
  • This textbook model adds the same public-currency amount to deposits and to reserves. Official aggregates have more detailed coverage and accounting conventions.
  • The reserve ratio is an input or an inferred accounting ratio, not a current legal reserve requirement. The retained 10 percent starting value is illustrative. Ratios above 100 percent are permitted.
  • All monetary amounts and the reserve ratio are nonnegative. Monetary base must be positive. With zero deposits, an observed reserve ratio cannot be inferred from zero reserves.
  • The multiplier is an accounting ratio for these stocks. It does not predict how much new lending or spending a reserve increase will cause.

Common questions

Is the multiplier always one divided by the reserve ratio?

Only in the model’s zero-currency special case with positive deposits. Public currency changes both money supply and the base.

Does the 10 percent default describe current policy?

No. It is a scenario input. Enter the ratio appropriate to the monetary stocks you are studying.

References

Bookify requires nonnegative monetary amounts and reserve ratios, with a positive monetary base for a defined multiplier.

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