What is the monthly interest rate if the annual is 12 percent?

Answer 1

Suppose the monthly rate is m% and the annual is a% = 12%

Then

(1 + m/100)12 = 1 + 12/100

so that 12*ln(1+m/100) = ln(1.12) = 0.1133

then ln(1 + m/100) = 0.1133/12 = 0.009444

therefore 1 + m/100 = exp(0.009444) = 1.00949

and then m/100 = 0.00949 so that m = 100*0.00949 = 0.949%

Note: you could have used log and powers of 10 instead of ln and and exp.