How to calculate interests in Brazil (CDI)

CDI - Definition

First of all, what is the so called CDI (terminology commonly used in the Brazilian market)?

In portuguese, CDI stands for "certificado de deposito interbancário" - free translation to english: interbank certificate of deposit. CDI is the average rate at which the Brazilian banks are willing to borrow/lend to each other for one day. This market is also called "interbank money market".

The equivalente to the CDI in the American market can be considered to be the FED Fund rate.

This rate is calculated by CETIP and published on a daily basis on the site https://www.cetip.com.br/?lang=en-us

Why Brazil uses the CDI

Before 1994 (year when Plano Real - economic plan that managed to control hyper inflation in the country - was launched),  Brazil used to suffered from extremely high inflation - CPI in the 12-months prior to the Plano Real was almost 5,000%!!!!. Due to this, long term planning was not possible, with most of the people trying to simply either buy something (cars, real estate, even groceries) as soon as they had some money or invest their money exclusively in short term investments - economic plans attempting to control inflation often confiscated the investments in financial products from the population, thus when investing in such products the population required the ability to exit at any moment if they suspected an economic plan was about to be implemented.

This problematic economic history created a "short term culture" in the economy, where people avoided long term planning and transactions are mostly referenced to the overnight interest rates - the CDI. Recently there were some discussions about why we still use the CDI and potential alternatives for this index. Tentatives were unsuccessful and CDI is still the major reference for the Brazilian economy what regards to nominal interest rates in local currency.


Calculation using the CDI

CDI is a rate expressed in an anual basis that uses the exponential business days day count convention. But...what exactly this means?

This means that (1) the CDI is a rate valid for business days only - weekends are not included in the day-counting process, and one year is considered to have 252 business days - and that (2) the calculation formula uses compounded interest calculation - differently from the international market where linear interest calculation is used. This calculation method compares to the IOS swaps, where the floating rate is reset on a daily basis.

If you make an investment with interest income referenced to the CDI, your income should be calculated as follows:

 There are, however, some transactions where variations of the CDI are negotiated, which are (1) the percentage of the CDI, and (2) a margin over the CDI. Each of those require a specific formula for the correct calculation of the interest amounts.

(1) Percentage of the CDI: no specific reason why Brazil uses this convention, but it is often used in loan transactions and deposits.

Interest amount should use the following formula:

(2) Margin over CDI: typically loan transactions use this convention, where a margin over the base rate is applicable for the calculation of the interest amounts. Formula for the interest amount as follows:

Interested in more information about the CDI and how financial products using this rate are calculated? Send me an email: mmatsmoto@gmail.com