02-Compounding

# 02-Compounding - Effective Rates/Stated Rates Effective...

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Effective Rates/Stated Rates

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Effective Rates/Returns Effective rate: the actual growth rate of an investment over a given period. Given one effective rate, you should be able to find the effective rate over another period. Example: Account pays 1% per month What is the effective annual return? Hint: the answer is not 12%!
Finding an Effective Returns Set the future value from investing at 1% per month equal to that from investing at rate r A per year. Then solve for r A . But FV=PV(1+r) n What PV should I use? It doesn’t matter! You will get the same answer regardless. Choose PV=\$1 for simplicity So I should set future values equal as of what time period in the future? Set future values equal as of any time period in the future and you will get the right answer. If two effective rates produce equivalent FV as of one future time period, then FV will be equivalent as of any time period.

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Effective Returns Suppose we set FV equal at the end of 1 year Account pays 1% per month: FV=(1.01) 12 Account pays r A per year: FV=(1+r A ) (1.01) 12 =(1+r A ) r A =(1.01) 12 -1=12.68% An account that pays 1% per month pays an effective annual return of 12.68%.
Effective Returns Suppose we set FV equal at the end of 2 years Account pays 1% per month: FV=(1.01) 24 Account pays r per year: FV=(1+r A ) 2 (1.01) 24 =(1+r A ) 2 Raise each side to the ½ power (1.01) 12 =(1+r A ) And we’re back to the same problem with the same answer as before It doesn’t matter at what future time period you set FV equal (1 year, 2 years, 3 years, etc.)

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Effective Returns Example: Account pays 24% every 3 years What is the effective annual return? Let
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## This note was uploaded on 03/01/2012 for the course BUS M 410 taught by Professor Brianboyer during the Fall '10 term at BYU.

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02-Compounding - Effective Rates/Stated Rates Effective...

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