# Effective Interest Rate

## Definition

Effective Interest Rate, EIR (also denoted Internal Rate of Return or Level Yield to Maturity) is in the context of IFRS 9 [1], the interest rate that exactly discounts estimated future cash payments or receipts through the expected life of the financial asset or financial liability to the gross carrying amount of a financial asset or the amortised cost of a financial liability.

## Calculation

For the calculation of an effective interest rate, estimates of expected cash flows consider all the contractual terms of the financial instrument (for example, prepayment, extension, call and similar options) but do not consider expected credit losses.

The calculation includes all fees and points paid or received between parties to the contract that are an integral part of the effective interest rate (see paragraphs B5.4.1–B5.4.3), transaction costs, and all other premiums or discounts.

## Formula

Given a set of expected cashflows ${\textstyle C_{i}}$ (with index running from 1 to n) and a set of discount factors D calculated using the compound effective interest rate over the expected life T of a financial asset, the effective interest rate (r) is derived by solving the equation

${\displaystyle {\mbox{GCA}}_{t}=\sum _{i=1}^{n}D_{i}(r)C_{i}}$

where the discount factor for period (i) is given by

${\displaystyle D_{i}={\frac {1}{(1+r)^{i}}}}$