How to Calculate Effective Interest Rates on Credit Cards

A credit card agreement typically specifies the annual percentage rate (APR) the credit is given at. However, if a credit card account has an outstanding balance during the entire year, an effective (actual) interest rate would be higher than nominal APR. It is because the interest is usually calculated (compounded) daily. Effective interest rate is calculated using the expression:
Effective Interest Rate (EIR) = 100% x [(1 + I)^n -- 1],
where I is the interest per compounding period (e.g. day) and n is the number of times interest is calculated per year (e.g. 365).
Example: Calculate EIR if APR is 16.5% and interest is calculated daily or monthly.

Things You'll Need

• Calculator

Instructions

1. Convert APR to decimal form.
   APR(f)=APR/100%.
   In our example, APR(f)=16.5%/100%=0.165.

2. Calculate interest (I) per compounding period n.
   I = APR(f)/n
   In our example, n is either 365 (daily) or 12 (monthly).
   I(d) = 0.165/365=0.000452055
   I(m) =0.165/12=0.01375

3. Calculate Effective Interest Rate (EIR) using the formula given above.
   In our example, for daily and monthly calculated interest:
   EIR(d)=100% x [(1 + 0.000452055)^365 -- 1] = 100% x 0.1793 = 17.93%
   EIR(m)=100% x [(1 + 0.01375)^12 -- 1] = 100% x 0.1781=17.81%.

   Effective interest rate is higher than APR by 1.43 and 1.31% and corresponds to the APR increase by 8.6 and 8%, respectively.

Resources

• Effective Interest Rate Calculator