Annual effective discount rate

The annual effective discount rate expresses the amount of interest paid/earned as a percentage of the balance at the end of the (annual) period. This is in contrast to the effective rate of interest, which expresses the amount of interest as a percentage of the balance at the start of the period. The discount rate is commonly used for U.S. Treasury bills and similar financial instruments.

For example, consider a government bond that sells for $95 and pays $100 in a year's time. The discount rate is

The interest rate is calculated using 95 as the base

For every effective interest rate, there is a corresponding effective discount rate, given by

or inversely,

Given the above equation relating ${\displaystyle \,d}$ to ${\displaystyle \,i}$ it follows that

or equivalently,

Since ${\displaystyle \,d=iv}$ ,it can readily be shown that

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