Monthly rate from an effective annual rate
v1tasa_anualtasa_mensualHow it is worked out
Turn an effective annual interest rate into the equivalent monthly rate, the one actually charged or earned each month.
An effective annual rate already includes compounding: it is how much one unit grows over a year, interest on interest included. To bring it down to a month you do not divide by twelve: you take the twelfth root of one plus the rate and subtract one. A 12 % effective annual rate works out to 0.9489 % a month, not 1 %.
The expression that runs
((1 + tasa_anual / 100) ^ (1 / 12) - 1) * 100The fields arrive with an example filled in: put your own numbers in and run it again. You can also edit the formula to fit your case.
What if the formula were yours?
This calculator is not hand-written: it is an Axioma formula. Open it in the editor to see how it is built, adapt it to your case and create the ones you need.
Step by step, from a 12 % effective annual rate
A 12 % effective annual rate is written as a factor: 1.12. That is a full year of growth, and what you want is the monthly factor that, repeated twelve times, gives the same thing. That is the twelfth root of 1.12, or 1.12 raised to the power of 1/12, which comes to 1.009489.
Take the 1 off the monthly factor and multiply by a hundred: 0.9489 % a month. Checking it is immediate: 1.009489 multiplied by itself twelve times gives 1.12 again, the 12 % for the year.
Why dividing by twelve gets it wrong
Twelve percent over twelve is 1 % a month, and 1 % a month for twelve months is not 12 %: it is 12.68 %, because every month charges interest on the interest from the months before. Dividing only works with nominal rates, which are precisely the ones that leave that compounding out.
The gap looks small over one month, but over a multi-year loan or a large deposit it adds up. Comparing an offer quoted as an effective annual rate with another quoted monthly, without converting them properly, is the usual way to pick the expensive one believing it is the cheap one.
Where effective annual rates show up
Savings accounts and deposits often advertise an annual percentage yield, which is an effective annual rate: it already counts the interest earned on interest. It is the figure meant for comparing products with different terms and compounding schedules.
Payments, on the other hand, happen month by month, and the interest in each one is worked out with the monthly rate. Converting is the first step to checking a card statement or working out a loan payment with the rate that is really being charged.
Frequently asked questions
- How do I turn a monthly rate into an effective annual rate?
- The other way round: add 1 to the monthly rate, raise it to the twelfth power and subtract 1. One percent a month is 1.01¹² − 1, a 12.68 % effective annual rate. It is the same calculation this tool does, walked in the opposite direction.
- What is the difference between a nominal and an effective rate?
- A nominal rate is an annual figure split evenly across periods: 12 % nominal compounded monthly is 1 % each month. The effective rate is what those periods add up to once compounded, and it is always higher than the nominal one when there is more than one period a year.
- Can I convert to a quarterly or daily rate instead?
- Yes, by changing the exponent: raise to 1/4 for a quarterly rate, since the year has four quarters, and to 1/365 for a daily one. Open the formula in the editor and swap the 12 for the number of periods you need.