How the annual vs monthly interest converter works

This calculator converts an interest rate from one period to the others: you enter the percentage, choose whether it is annual, monthly or daily, and it shows the three equivalent rates. Use it to compare a loan quoted per month with an investment quoted per year, to find out how much an annual rate yields per month, or to fill in other calculators that ask for the rate in a different period.

Equivalent rates produce the same final amount over the same term when interest is compounded, that is, when the interest earned in each period also earns interest. The relation is (1 + ia) = (1 + im)^12 = (1 + id)^365, with the rates as decimals; therefore im = (1 + ia)^(1/12) − 1 and id = (1 + ia)^(1/365) − 1. The daily rate uses 365 calendar days, not the 252 business days used in financial markets. Dividing the annual rate by 12 is only valid for simple interest (a nominal rate) and overstates the equivalent monthly rate.

Example: 12% per year is equivalent to 0.9489% per month and 0.0311% per day. The other way round, 1% per month is equivalent to 12.6825% per year, not 12%. Results are rounded to four decimal places. Taxes, fees and inflation are not included. Educational tool, not financial advice.