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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. 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

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

  2. 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.

  3. 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%

  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) = 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.

  5. 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%

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