Excessive Interest Rate Definitions


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Excessive Interest Rate Definintions

Annual interest rate (AIR)
Effective interest rate (EIR)
Compounding
Present value (PV)
Future Value (FV)

The AIR is the number most often quoted in the newspaper. It is often called the nominal interest rate when the compounding frequency is quoted along with it. In the USA its often and incorrectly called the APR. The APR, by definition, is the new AIR once all the costs of the loan or mortgage are factored in and it is therefore higher than the AIR.

The EIR is the same as the AIR only when the compounding is “annual compounding”. If the compounding is more frequent than annual compounding then there is an EIR associated with every AIR. As the compounding becomes more frequent the EIR increases. An AIR of 12 % with monthly compounding has an EIR of 12.6825% whereas the EIR is 12.7474% with daily compounding. Strictly speaking, “a 12% mortgage with monthly compounding” does not mean your mortgage interest is compounded monthly. What it really means is that if you miss your monthly payment the interest is compounded monthly. The incorrect nomenclature is so deeply rooted in the Canadian and American financial industry it seems impossible to correct the sloppy vernacular.

The Present Value and Future Value are exactly related by a mathematical equation over a stated period of time. If the period of time is years, then the interest rate from the equation is the interest rate for the year and by definition that is called the effective interest rate, EIR. Time and money are exactly related and Einstein referred to this as the 8th wonder of the world.

(Screenshot 1)

If you borrow $10,000 at 12% for one year and the lender is using monthly compounding then the monthly payments as per the calculator (green) would be $888.49. If you decided not to make payments then the interest is compounded monthly and added to the outstanding balance. At the end of one year you owe the lender $11,268.25 as shown by the negative amortization schedule. Notice how the PV/FV calculation shows the same EIR as the green calculator. In other words the Principal in the green calculator is the PV and line 12 of the negative amortization schedule is the FV. By adding 1.0 to the decimal EIR (1.0 + 0.126825) and multiplying it by the initial Principal (PV) the FV of $11,268.25 is obtained. The effective interest rate is the true rate a lender can theoretically yield because it is based upon the premise that the lender reinvests your monthly payments as he receives them each month.