How to calculate interests in Brazil (CDI) - Part 4

After discussing what "CDI" and "percentage of CDI" are, to finalize this topic we will talk about the "margin over CDI".

In the USD market, US Libor loans are often negotiated on a Libor + margin basis. "Margin over CDI" is the equivalent to Libor + margin in Brazil. One should probably ask: if these two are equivalent, why do we need a post about this topic?

Answer is: although these two are equivalent, the calculation process is not.

Formula for calculating interests using "margin over CDI" follows below:

Similarly to the numeric example provided in my previous post, the calculation process for "margin over CDI" starts with the daily compounding of the CDI.

Assuming that we have a loan of 100,000 BRL at CDI + 1% and that the CDI for the first day of the loan is 11%, then the interests calculation for this first day would be:

Balance of your loan at day one: 100,045.37 BRL

Assuming that the CDI for day two is 11,25%, interests calculation should be:

Balance of your loan at day two: 100,091.66 BRL

After one month (21 business days), the balance of your loan should be 100,961.10 BRL:

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

How to calculate interests in Brazil (CDI) - Part 3

Do you know what "percentage of CDI" means? No? You're not the only one...😃

In Brazil, investments, derivatives, loans and other financial contracts are often negotiated using as contractual rate (or reference rate) "percentage of CDI". But, what exactly is "percentage of CDI"?

As previously discussed here, CDI is the average rate at which Brazilian banks are willing to borrow/lend to each other for one day. This is the benchmark rate for the BRL domestic market.

"Percentage of CDI" is the discount/premium over the regular CDI rate. For example, when a bank extends a loan to a customer at 120% of the CDI, this means that the cost of this loan is 20% higher than the regular CDI rate. On a deposit transaction at 90% of the CDI, the yield on this investment is 10% lower than the regular CDI.

Negotiating interest rates using "percentage of CDI" is a specificity of the BRL domestic market. Market professionals often say this is related to historical reasons, mostly linked to the super high inflation (and consequently high interest rates) we used to have in the country some decades ago. Since prices and interest rates used to oscillate significantly on a daily (even intraday) basis, negotiating a fixed margin over the benchmark rate was not a reliable metric (imagine a margin of 1% over a rate of 10% and, on the following day, 1% over a rate of 100%). Percentage of CDI provides a return that varies depending on the prevailing interest rate levels, what worked better at that time for investors.

Coming down to math, this is the formula for calculating interests using "percentage of CDI":

Similarly to the numeric example provided in my last post, the calculation process for "percentage of CDI" starts with the daily compounding of the CDI.

Assuming that we have an investment of 100,000 BRL at 90% of CDI and that the CDI for the first day of the investment period is 11%, then the interests calculation for this first day would be:

Balance of your investment at day one: 100,037.28 BRL

Assuming that CDI for day two is 11,25%, interests calculation should be:

Balance of your investment at day two: 100,075.38 BRL

After one month (21 business days), the balance of your investment should be 100,789.35 BRL:

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