02-Compounding

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

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Effective Rates/Stated Rates
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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%!
Background image of page 2
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.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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%.
Background image of page 4
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.)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Effective Returns Example: Account pays 24% every 3 years What is the effective annual return? Let
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 27

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

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online