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Keep the horizon in years
A discount factor is dimensionless, while its date gives the accumulation horizon. D = 0.90 at three years and D = 0.90 at one year describe different annual rates. The same present-to-future ratio is spread over different durations.
Invert the accumulation equation
Starting from D = (1+s)^−T, raise D to −1/T to recover 1+s. Positive D is required for this real-valued effective-rate transformation.
This is an annual effective quotation, not a simple discount rate.
Compare another possible quotation
For D = 0.90 and T = 3, the annual effective rate is approximately 3.574417%. A continuously compounded zero on the same factor is −ln(0.90)/3, approximately 3.512017%. Different quoted percentages can represent the same dated factor.
| Convention | Annual rate |
|---|---|
| Effective annual | 3.574417% |
| Continuous | 3.512017% |
Round at the output rather than the factor
Rebuild D from the unrounded rate and original T. A displayed rate rounded to two decimals may not exactly reproduce a high-precision price. Retain the original factor for pricing and use rounded rates for presentation.