Question

A credit card advertises an annual interest rate of 23%.

Answer 1

In one year
1 + (23/100) = (1 + x)^12
1 + 0.23 = (1 + x)^12
(1 + x)^12 = 1.23
1 + x = 1.23^(1/12)
x = 1.23^(1/12) - 1
x =~ 0.017400841772181508280113627030242
That's about 1.74% per month (which is about 20.881% per year), compounded monthly, to equal 23% per year, compounded annually.


So I believe you can write
I=(1+.0174)12torI=1.017412t

Answer 2

 the monthly rate is:

[1 + 23%]^(1/12) =1.23^(1/12) =1.0174 - 1 x 100 =1.74%