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Label every covered interval
For three annual intervals, f01 covers today to year one, f12 covers year one to two, and f23 covers year two to three. The subscript names both ends; it does not merely identify an arbitrary column of rates.
Compound the intervals
Use f01 = 4%, f12 = 6.009615%, and f23 = 8.028662%. Their accumulation product is 1.06³. A payment at year two uses only the first two factors, while a year-three payment uses all three.
Annual effective one-year forwards use multiplicative accumulation.
Use the factor at the actual payment date
Each coupon is discounted by the forward product ending on its own date. Applying all three factors to the first coupon wrongly moves its valuation horizon. This is a schedule error even if the final principal happens to be discounted correctly.
Separate a curve identity from a future observation
These forwards are implied by today’s stipulated curve. They reconcile alternative accumulation schedules under the pricing model. They are not a guarantee that the future one-year market rate will equal the implied number. Risk premia and subsequent information can matter.