Discount Rate - Annual Effective Discount Rate

Annual Effective Discount Rate

The annual effective discount rate is the annual interest divided by the capital including that interest, which is the interest rate divided by 100% plus the interest rate. It is the annual discount factor to be applied to the future cash flow, to find the discount, subtracted from a future value to find the value one year earlier.

For example, suppose there is a government bond that sells for $95 and pays $100 in a year's time. The discount rate according to the given definition is

The interest rate is calculated using 95 as its base:

For every annual effective interest rate, there is a corresponding annual effective discount rate, given by the following formula

or inversely,

where the approximations apply for small i and d; in fact i - d = id.

See also notation of interest rates.

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