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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

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effective interest rates

Effective Interest Rates

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

nominal and effective interest rates
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
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 = (1+0.169/365)365 –1 = 0.184 = 18.4%
continuous compounding
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) = erN
  • Since (F/P,i,N)= (1+i)N in the discrete compounding case, we can set er = 1+i and we get i = er - 1. This is the equivalent interest rate.
credit card revisited
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 = e0.169–1 = 0.18412 = 18.412%
  • r=16.9%/year, M= 365/year
  • i = 18.407%