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
