I wish to double my investment at a rate of 6% compounded continually, how many years will that take?

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• I got the very same, but when comparing to 6 percent monthly I got 11.58 yrs.
  log(2)/12log1.005 .....1.005=1+(.06/12)
  and generally ln2/rate gives 11.55 meaning decay constant over rate?
  
  Thanks

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  by archimedes on November 19th, 2009

• to get the equivalant of annual 6% increase as a per month percentage you can't divide the 6% by 12 months because the new percentage will still be compounded (though compounded monthly).
  
  x(y^n) = 1.06x
  x = your investment
  n = no months = 12
  y = monthly percentage rate
  
  x(y^12) = 1.06x
  y^12 = 1.06
  y = 1.06^(1/12)
  y = 1.00486755 = 0.486755% monthly interest.
  
  CHECK: x(1.00486755^n) = 2x
  x = your investment
  n = no of months
  x(1.00486755^n) = 2x
  (1.00486755)^n = 2
  log(1.00486755^n) = log 2
  n.log1.00486755 = log2
  n = log2/log1.00486755 = 142.75 months
  142.75/12years = 11.9 years

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  by Jahono on November 20th, 2009

• A=P(1+r/t)^nt
  2=1(1+.06/12)^nt
  this is for a monthly compound I was trying to determine which would double my chunk the quickest I follow you until the last step with the 12 years the idea I thought was to seek years and tus they would not be a variable, unless you itended 12 months
  Thnks my banker is a moron, think he's looking out fro his own interest and got pissy when someone knew how to do more than balance a checkbook

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  by archimedes on November 20th, 2009