# Effective Interest Rate from bifurcated interest rate

Here goes, this is the scope of my question: Say I want to take out a credit card, that has 0% interest for 12 months, when at the 13th month, whatever debt is taken out on the card will be subjected to a 12% APR finance charge from then after. Lets say the card compounds monthly.

If I know the length of time I want to hold the debt say 3 years out from today, ie, 12 months of 0% interest, and 24 months at the 12% situation, how do I calculate the effective annual interest rate of the card accounting for the real situation that it is 0% apr for 1 year. I'm not asking how to convert 12% apr monthly compound to effective annual interest, rather I want to know what is the EAR accounting for both of these interest periods. Thanks!

• Actually, I should say how do i calculate the EAR in this situation. Thanks! Jul 25, 2015 at 1:01
• Easiest way is to work out the real interest paid, then calculate backwards from that to a single rate,. Dec 16, 2015 at 14:34

If the APR is an effective rate.

Interest over 3 years = (1 + 0.0) (1 + 0.12) (1 + 0.12) - 1 = 25.44 %

Effective annual rate = (1 + 0.2544)^(1/3) - 1 = 7.84798 %


If the APR is a nominal rate compounded monthly, first convert it to an effective rate.

r = (1 + 0.12/12)^12 - 1 = 0.126825

Interest over 3 years = (1 + 0.0) (1 + r) (1 + r) - 1 = 26.9735 %

Effective annual rate = (1 + 0.269735)^(1/3) - 1 = 8.28568 %

• By definition, APR is not what you are calling an "effective rate". APY is what you are calling an "effective rate". Dec 16, 2015 at 23:50
• @Jasper - It depends on country, e.g. Factsheet: APR, AER and EAR. Dec 17, 2015 at 0:25
• See also APR: European Union, where APR is defined as the effective rate. Dec 17, 2015 at 7:26