find x % needed to double value in 5 years?

[Dillinger4]

A 100 percent increase over five years is a compound annual growth rate of approximately 15 percent a year. How would i find the percent needed? (10 * 1.15)⁵ = 20 is correct but how do i get the %? Thanks.

[Dillinger4]

I think i have it.

% CAGR = ((Ending Value / Initial Value) ^ ( 1 / # of periods) - 1) * 100

((20/10) ^ (1/4)-1) *100 = 59.5

59.5/4 = 14.9%

Is there a simpler way to find out the % needed to double a know value over a period of time? (10 * x)⁵ = 20

[alkatran]

base * (1+interest)^years = total

1 * (1+x)^5 = 2
1 + x = 2 ^ (1/5)
x = 2 ^ (1/5) - 1 =~ .1487 = 14.87%

[Dillinger4]

Seems pretty clear except for the line.
base * (1+interest)^years = total

1 * (1+x)^5 = 2
1 + x = 2^(1/5)
x = 2 ^ (1/5) - 1 =~ .1487 = 14.87%

I understand that you have to shift everything to one side to isolate x
but how is the power shifted? if the power is ^ 5 why does it end up being ^ 1/5? Thanks for the help.

[opus]

A power of 1/5 is the same as the fifth root!

So you have (a)^5=b , take the fifth root of both and you have
a=(b)^1/5.

[Dillinger4]

Ah ok i see now. Pretty cool.