The final rate is calculated by taking the arithmetic average of 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 arithmetic average assumption to calculate the interest A accruing over Δt for a unit notional as:
A = r₁Δt₁ + r₂Δt₂
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