What is the effective monthly interest rate for a loan with

What is the effective monthly interest rate for a loan with a 8% APR if the loan is compounded daily, monthly, and continuously and you make monthly payments on the loan?

Solution

Compounded daily:

daily interest rate = 8%/365 = 0.022%

effective monthly interest rate = (1 + 0.022%)³⁰ - 1 = 0.66%

Compounded monthly:

monthly interest rate = 8%/12 = 0.667%

effective monthly interest rate = 0.667%

Compounded continuously:

effective monthly interest rate = (exp)^{8% x 1/12} - 1 = 0.669%