How to Convert an Annualized Federal Funds Rate to Overnight Interest
Summary
The document clarifies that the Federal Funds rate is quoted on an annual basis even though it refers to overnight lending between depository institutions. To calculate interest on a one-day loan, the annualized rate is applied using the Actual/360 day-count convention. For example, at an annual rate of 0.5%, interest on one dollar borrowed for one day is 0.005 divided by 360 dollars.
This distinction resolves the question of whether the quoted rate should be divided by 365 or converted through daily compounding: the answer identifies the market convention rather than deriving a compound annualization formula. The explanation is specific to the stated U.S. money-market context. It does not cover how other countries quote policy rates, how the effective Federal Funds rate differs from the target range, or conventions for other instruments, so those details require separate treatment.
Key ideas
- The Federal Funds rate is quoted as an annualized rate despite referring to overnight lending.
- The stated day-count convention for this calculation is Actual/360.
- For a one-day loan, apply the annual rate to one day using 360 as the denominator.
- Rate conventions vary across markets and instruments, so this explanation should not be generalized without checking the relevant convention.
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# Central bank interest rates: are they quoted annualized? # Central bank interest rates: are they quoted annualized? After a little research on interest rates of different countries I figured out that they are more complicated than I thought and the meaning of them varies country by country. For example, the U.S. rate, that has just been rised to 0.5%. Global-rates.com states: When reference is made to the US interest rate this often refers to the Federal Funds Rate. The Federal Funds Rate is the interest rate which banks charge one another for 1 day (overnight) lending. This American base rate is set by the market and is not explicitly laid down by the FED. By withdrawing or adding funds to the money supply the FED tries to bring the effective federal funds rate into line with the interest rate that it is striving for. If the FED’s monetary policy alters the base rate, that usually affects the interest rate on various products such as mortgages, loans and savings. So, the U. S. interest rate is the FED Funds Rate, which is not an actual (effective) rate, but rather a target rate, set by The Federal Open Market Committee (FOMC). Wikipedia defines federal funds rate as following: In the United States, the federal funds rate is the interest rate at which depository institutions (banks and credit unions) lend reserve balances to other depository institutions overnight. Thus, FED Funds rate is also an overnight rate. What does it really mean mathematically for FED Funds rate to be 0.5 %? If it is annualized (overnight -> annual), in what way exactly? Is the simple interests formula (R = i * t) used, meaning that FED really wants an actual overnight rate to be 0.5% / 365 (365 days in a year)? Or maybe the compound interest – R = (1+ i / n)n – is used? If so and if compounding period would be one day (is it in this case?), we'd find an an actual interest rate that FED wants to be by solving equation 0.5 = (1*x/365)^365. Thank you in advance. ## Answer by nbbo2 (score 9) https://quant.stackexchange.com/a/22402 Fed Funds are quoted on an annual basis so 0.5% means half a percent per year. The day count convention used is Actual/360 (note the use of 360, not 365 or 365.25. This old convention is common to many US money market instruments). So if you borrow 1 USD for a single day you would pay 0.005/360 in interest.
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