6.3 Comparing Rates: The Effect of Compounding

How to calculate the stated/quoted interest rate

= the interest rate changed per period x the number of periods per year

Mortgages

Common example of annuity with monthly payments - Although payments are monthly, regulations for Canadian financial institutions require that mortgage rates be quoted with semiannual compounding - Financial institutions offer mortgages with interest rates fixed for various periods ranging from 6 months to 25 years (borrower chooses the period for which the rate is fixed)

EAR formula

EAR = [1 + (stated rate/m)]^m -1 m = the number of times the interest is compounded during the year

EAR formula for continuous compounding

EAR = e^(stated rate) - 1 e = exponential

Effective annual rate (EAR)

The interest rate expressed as if it were compounded once per year

Stated interest rate (or Quoted interest rate)

The interest rate expressed in terms of the interest payment made each period

compounded monthly

compounded 12 times per year

compounded daily

compounded 365 times per year

compounded quarterly

compounded 4 times per year

compounded annually

compounded once per year

compounded semiannually

compounded twice per year

Annual percentage rate (APR)

the interest rate charged per period x the number of periods per year