Example: Effective Annual Interest Rate

Assume the 1-month interest rate is quoted at 6%. You make a deposit of $100 and at the end of every month, you re-invest the balance at the one-month rate. What is the effective annual interest rate (EAR)?

Solution:

1-month interest rate = 1/12*6% = 0.5%

EAR = 1.005^12 1 = 0.0617 or 6.17%

Note the use of compounding to work out the EAR.

Hi guys, the above question is the example that I got from my lecture note. I need a few explanations here as I have difficulty understanding.

Is 6% an annual percentage rate? If it is, the question doesn't say it is an APR. I thought APR was supposed to be presented as ANNUAL, not a 1-month interest rate.

Also, where do the "-1" and "^12" come from at "EAR = 1.005^12 -1"? I am confused. Can you explain it in detail?

Thank you.