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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 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 semiannual 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 semiannual 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.

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