Calculator to convert a monthly interest rate into an effective annual rate

The formula: from monthly to effective annual

A monthly rate compounds: every month the interest is added to what you owe, and the next month charges interest on it too. That's why the effective annual rate isn't the monthly rate times 12. It's 1 plus the monthly rate, raised to the 12th power, minus 1.

An example: 2% a month isn't 24% a year, it's 26.82% effective annual. That's the example Colombia's Financial Superintendency gives: 24% nominal annual paid monthly equals 26.82% effective annual. Brazil's central bank does the same math with 1% compounded monthly, which comes to 12.68% a year.

To go the other way, from effective annual to monthly, you do the opposite: 1 plus the effective annual rate, raised to the power of one twelfth, minus 1. The calculator does both with every decimal and shows you the rounded result.

Sources for this part:Superintendencia Financiera de Colombia, Banco Central do Brasil

Nominal and effective: why they aren't the same

The nominal annual rate is a reference: the monthly rate times 12, without counting that interest is added to the debt. The effective rate does count it, which is why it's higher when interest is charged every month.

Argentina's central bank puts it this way: what a person really pays on loans is the effective rate, which is calculated from the nominal rate as long as there are no other costs. Colombia's Financial Superintendency describes the effective rate as the annual expression of the nominal interest, depending on how often it is paid.

In Colombia, the Financial Superintendency has said that credit rates are stated in effective annual terms. In the United States, credit cards state their interest as a yearly rate called the APR, according to the Consumer Financial Protection Bureau. If your document says nominal and interest is paid monthly, at the end of each month, choose “Nominal annual”. A quarterly or paid-in-advance nominal rate can't be converted here. Argentina's TNA and a card APR with a daily rate have their own options: we explain each one below.

Sources for this part:Banco Central de la República Argentina, Superintendencia Financiera de Colombia, Superintendencia Financiera de Colombia, Consumer Financial Protection Bureau

Argentina: from TNA to TEA, the BCRA way

In Argentina, every credit document must show the effective annual rate, and the central bank (BCRA) gives the formula: 1 plus the TNA times the days in each period divided by the year's divisor, raised to the divisor divided by the days in the period, minus 1. With monthly installments, each period counts as 30 days. The general divisor is 365 days; some home mortgages and car-secured loans use 360.

So a 73% TNA is a 103.18% TEA with the general 365-day divisor; with 360, the one some mortgages and car-secured loans use, it's 103.13%.

Each month your bank applies the TNA divided by 12; the TEA on your statement counts 30-day months, which is why, with the 365 divisor, it comes out a little higher than compounding 12 times. Choose “Argentina's TNA” above and the divisor in your contract.

Sources for this part:Banco Central de la República Argentina

United States: the APR and the daily rate

Some card issuers calculate interest with a daily periodic rate, the APR divided by 360 or 365 depending on the issuer, and add it to the balance, so interest compounds daily, the CFPB explains. Many card companies work out the interest you owe daily, based on your average daily balance.

Check your card agreement: at a 24% APR, the effective rate is 27.11% (÷365) or 27.54% (÷360); if your card uses a monthly rate, 26.82%. Choose “Card APR with a daily rate” and the divisor in your contract: the calculator doesn't guess it.

Under Regulation Z, the APR is each periodic rate multiplied by the number of periods in a year. That's why, for a card with a monthly rate, “Nominal annual” is exact: a 24% APR is 2% a month.

Sources for this part:Consumer Financial Protection Bureau, Consumer Financial Protection Bureau, Consumer Financial Protection Bureau

What this calculator leaves out

It converts the interest rate, nothing else. Costs that aren't interest, like insurance, an annual card fee or a commission, aren't included. That's why it doesn't work for Mexico's CAT or Argentina's total financial cost: those figures already add other costs.

Bank of Mexico defines the CAT as a standardized measure of the cost of financing, expressed as an annual percentage, that includes all the costs and expenses of the credit. And Argentina's central bank explains that the total financial cost is made up of the nominal annual rate plus all the costs tied to the operation.

Sources for this part:Banco de México, Banco Central de la República Argentina

How it helps with your debts

With the effective annual rate you can compare two loans even if one gives you a monthly rate and the other an annual one: the one with the lower effective annual rate charges less interest, if the other costs are the same.

In Oslo, when you add a debt you type the rate as it appears on your statement, monthly or annual, and the app converts it with the same formula as the “Monthly”, “Effective annual” and “Nominal annual” options for every calculation it makes with that debt.