3.4 Effective Interest Rate
Effective interest rates can be used to compare investment opportunities. The effective rate of interest is the equivalent rate of simple interest earned over one year for an interest rate that is compounded twice or more over the year. The annual simple interest rate will be greater than the annual compounding interest rate to earn the same amount of interest.
The annual interest rate, r, for compounding calculations, is often called the nominal rate.
Illustration: If RM1 is deposited at 4% compounded quarterly, the compound amount is RM1.0406, an increase of 4.06% over the original RM1. Here, the actual increase of 4.06% in the money is somewhat higher than the stated increase of 4%. To differentiate between these two numbers, 4% is called the nominal or stated rate of interest, r while 4.06% is called the effective rate, 
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The effective rate corresponding to a stated rate of interest r compounded m times per year can be calculated as follows:
(1) 
Betty needs to borrow money. Bank A charges 8% interest compounded semiannually. Bank B charges 7.9% interest compounded monthly. At which bank will she pay the lesser amount of interest?
