Annual ⇄ Monthly Rate Converter

How to convert between periodic interest rates

To find equivalent compound rates, use i_year = (1 + i_month)^12 − 1, or its inverse i_month = (1 + i_year)^(1/12) − 1. When the rate is stated per business day (the Brazilian convention counts 252 business days a year), the exponent jumps to 252: i_year = (1 + i_bd)^252 − 1. Watch out for nominal rates, meaning the annual rate divided by 12. That gives a simple-interest figure that shows up in some contracts, but it is not the real effective conversion.

Take a CDB advertised as "1% per month". It really yields (1.01)^12 − 1 = 12.68% per year, not the 12% you might expect. Selic at 14% per year works out to about 1.096% per month and 0.052% per business day. By convention CDI is measured per business day, whereas Selic Meta is quoted annually on a 252-business-day year.

Practical applications

Before any comparison means anything, you have to bring the rates onto a common period. That holds whether you are weighing investments with different terms (a monthly CDB against an annual LCI), deciding if you should move between products, working out the Total Effective Cost (CET) on a loan, or laying out a Price-table amortization schedule.

FAQ

Why 252 business days instead of 365? In Brazilian fixed-income markets (CDI, Selic Over), interest only accrues on trading days. ANBIMA settled on 252 as the standard, which is roughly how many trading days a year survives once you strip out weekends and bank holidays.

Can I just divide an annual rate by 12 to get the monthly? Do that only when the contract spells out "nominal rate". It is simple interest and ends up understating the true monthly effective rate. For compound equivalence, reach for the 1/12 exponent every time.

What is the difference between Selic Meta and Selic Over? Selic Meta is the target Copom sets, annualized on a 252 bd basis. Selic Over is the realized daily average of repo operations, which sits a touch below the Meta. CDI follows Selic Over closely.