An annual interest rate can be referred to or written as,

12 % annual interest rate

12 % annual interest rate, compounded monthly

The latter phrase is the one you will see printed in the newspapers, and the front of mortgage payment booklets, and is usually called the nominal interest rate. If the annual interest rate is quoted along with the compounding method then it is customarily called the nominal interest rate.

In order to compare interest rates the compounding method must be stated along with the rate. For every annual interest rate (AIR) there is a corresponding effective interest rate that depends upon the compounding method. For example, an American mortgage with an annual interest rate of 12% with monthly compounding has an effective interest rate of 12.6825%. A Canadian mortgage with an annual interest rate of

12% with semi-annual compounding has an effective interest rate of 12.36%. The Canadian mortgage is a better deal for the borrower because the effective interest rate (EIR) is lower. Bottom line, if a Lender offers you a 12% rate with either monthly or semi-annual compounding, you should take the semi-annual compounding option as it will cost less in interest

because of the lower effective interest rate. The borrower always pays more in interest with a more frequent compounding method. Using mathematical vernacular, Effective Interest Rates, EIR, are always considered to be on an annual basis. The effective interest rate is always greater than the nominal rate.

When the compounding method is annually the effective interest rate and the nominal rate are identical.

The advantage of quoting effective interest rates is one does not need to be concerned about the type of compounding. An effective interest rate, EIR, can stand on its own merit. If someone offered you a one year loan of $1000 at an effective interest rate of 12.36% you would owe the lender $1,123.60 at the end of the year. This same loan could have been given to you at 11.7106% with monthly compounding or 12% with semi-annual compounding. The two loans are identical because they both have an effective interest rate of 12.36%. In other words an annual interest rate of 11.7106% with monthly compounding is exactly equivalent to an annual interest rate of 12% with semi-annual compounding. Both loans require you to pay back $1,123.60 at the end of the year. In this screenshot you can see that both loans due to deemed reinvestment (negative amortization schedule) lead to the same thing for the lender, because the EIR is the same!

In summary the APR does not mean effective interest rate, EIR. The APR has absolutely nothing to do with the effective interest rate, EIR, by definition. In financial circles the EIR is meant to mean one thing and one thing only, … the actual interest rate at the end of the year because of the compounding frequency, nothing more nothing less.