Effective Interest Rates

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# Effective Interest Rates - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Effective Interest Rates' - Anita

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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
• 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 = (1+0.169/365)365 –1 = 0.184 = 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) = 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
• 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%