Effective Interest Rates You’d be surprised what you are paying for credit card debt

Nominal and Effective Interest Rates The nominal interest rate ( r ) is an interest rate compounded more than once an year, but quoted on an annual basis –Example: 16%/year, compounded quarterly The effective interest rate ( i ) is the interest rate that when compounded once a year would yield the same return as a nominal rate compounded more than once a year. –Example: 16%/year divided by 4 = 4%/month. The effective annual rate is 16.99%/year – i = (1+r/M) M -1 where M is the number of compounding periods per year.

Example of Nominal vs Effective A credit card company advertises an A.P.R. of 16.9% compounded daily on unpaid balances. What is the effective interest rate per year being charged? r =16.9%/year, M = 365 days/year i = ( /365) 365 –1 = = 18.4%

Continuous Compounding In most business transactions, interest is compounded at the end of discrete periods of time. However, in most enterprises, cash flows in and out almost continuously. Therefore, continuously compounding is sometimes used. With continuous compounding, (F/P,r%,N) = e rN Since (F/P,i,N)= (1+i) N in the discrete compounding case, we can set e r = 1+i and we get i = e r - 1. This is the equivalent interest rate.

Credit Card Revisited A credit card company advertises an A.P.R. of 16.9% compounded continuously on unpaid balances. What is the effective interest rate per year being charged? r =16.9%/year, M =  /year i = e –1 = = % r =16.9%/year, M = 365/year i = %