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Read the compatible instrument prices
All prices are per 100 final principal on a common valuation date. The first instrument has one payment of 100 at year one. The second pays 5 and 105. The third pays 6, 6 and 106. Assume all promised payments occur and ignore transaction costs.
Solve the factors in order
The zero yields 96/100 = 0.96. Next, D2 = (99 − 5×0.96)/105 = 0.897143. Finally, D3 = (101 − 6×0.96 − 6×D2)/106 = 0.847709. Retain the unrounded D2 in the last calculation.
Reconstruct the complete payment equations
| Instrument | Calculation | Price |
|---|---|---|
| One-year zero | 100 × D1 | 96 |
| Two-year coupon | 5 × D1 + 105 × D2 | 99 |
| Three-year coupon | 6 × D1 + 6 × D2 + 106 × D3 | 101 |
Translate factors only after the price checks
The implied annual effective zeros are 4.166667%, 5.576971%, and 5.661739%. They are outputs from these original fictional prices, not current market data. Price reconciliation checks consistency with the selected instruments, not every modeling assumption.