The final rate is calculated by compounding the intermediate rates.
For example, assume a coupon accrual period Δt consisting of two consecutive sub-periods of lengths Δt₁ and Δt₂
We are also given the rates (index fixings) r₁ and r₂ that are responsible for the interest accruing over Δt₁ and Δt₂ respectively.
At first we use the compounding assumption to calculate the interest amount A accruing over Δt for a unit notional as:
A = (1 + r₁Δt₁)(1 + r₂Δt₂) - 1
The above formula may be easily extended to more than two sub-periods.
Then the effective average rate over the whole period Δt is defined as the ratio:
r = A/Δt