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Recognize the shortcut
Two successive one-year forwards of 10% and 20% do not give a two-year accumulation of 30%. That sum omits the second year’s return on growth accumulated in the first year. Both dates and interval conventions matter.
Multiply the two factors
Starting with 100, the first interval ends at 110. The second interval applies 20% to 110, producing 132. The total interval growth is 32%, and the equivalent annual effective spot is √1.32 − 1, approximately 14.891253%.
| Quantity | Result |
|---|---|
| Arithmetic sum | 30% |
| Two-year total growth | 32% |
| Equivalent annual effective rate | 14.891253% |
Use the discount factor as a cross-check
A 132 final amount discounted through the factors 1.10 and 1.20 returns 100. A denominator of 1.30 does not. This reconstruction exposes the shortcut without needing an actual market forecast.
Keep total and annualized growth distinct
Multiply all covered accumulation factors, then annualize over the total duration if required. A mean of the two quoted rates is another different shortcut. For unequal interval lengths, use the corresponding powers before converting the combined horizon.