Solving for Time in a CAGR Calculation

[212]

I know the Final Value (100) and the Starting Value (1), and I know the Compound Annual Growth Rate (100%). But how do I calculate the time ("N" in the equation below) needed to achieve this?

I guess another way I might be able to simplify this example is: 1*2^6.644 = ~100. But how do I solve for the "6.644" here?

I've been looking around on Google for variations of the CAGR formula, but I can't seem to find this one.

I'm guessing this may involve logarithms, but it's only a guess. In case that's true, do you know how to write it in an Excel formula (which is ultimately what I'll use it for).

Thanks for your help!

 

[BigBeachBanana]

[math]CAGR=\Bigg(\frac{Final}{Start}\Bigg)^{\frac{1}{N}}-1\\ 1+CAGR=\Bigg(\frac{Final}{Start}\Bigg)^{\frac{1}{N}}\\ \ln (1+CAGR)=\frac{1}{N}\cdot \ln \Bigg(\frac{Final}{Start}\Bigg)\\ N=\frac{\ln \left(\frac{Final}{Start}\right)}{\ln (1+CAGR)}\\[/math]In excel, use =LN function for natural log and the rest is just cell reference to your final value, starting value, and CAGR.
=LN(FinalValue/StartingValue)/LN(1+CAGR)

 

[212]

Wow -- thank you so much!

I'm truly impressed by your answer, and thanks for trying to explain it a bit.

I took Calculus AB and BC over 25 years ago -- clearly, I'm quite rusty. But thank you so much for taking the time to provide me with a solution -- I've been looking for one for a while. At the end of the day, we still can't "Google" everything -- we need people like you know really know and understand this stuff.