Which is the interest rate that a bank or lender is required by law to use: APR or Effective Rate?

Question

And are they required to quote the annual rate (one compounding period)? So if you are offered a loan that the bank writes in fine letters would be compounded monthly: What happens to the rate (r) and the period (t)? (that is how are you going to adjust those in your formula before your calculation?)

Answer 1

Bank are required to disclose both the annual Percentage Rate (APR) and the Annual Percentage Yield (APY). The first is the nominal rate that the bank is charging and the second is what you pay (the effective rate) after taking compounding into consideration. In other words banks are not using one or the other but the first rate, after compounding, leads to the second rate in annual terms.

If the rate (r) is 12% and compounding is monthly then 12%/12mo, or 1%, would be compounded each month. Mathematically, the APY would be calculated by 1.01 to the twelfth power minus 1. (1.01^12 - 1) resulting in 12.68%.