## Compound

Subtype of Build RuleThe final rate is calculated by compounding the intermediate rates.

For example, assume a coupon accrual period

**consisting of two consecutive sub-periods of lengths**

*Δt***and**

*Δt₁*

*Δt₂*We are also given the rates (index fixings)

**and**

*r₁***that are responsible for the interest accruing over**

*r₂***and**

*Δt₁***respectively.**

*Δt₂*At first we use the compounding assumption to calculate the interest amount

**accruing over**

*A***for a unit notional as:**

*Δt*

*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

**is defined as the ratio:**

*Δt*

*r = A/Δt*