need help with math

[asauer]

I have a pretty dumb math question about figuring out my FIRE date.  I think I'm making this harder than it is. I know my start amount (420K), I know my goal amount (1.3M) and about how much I'll invest per month (7K).  I'm missing the rate of return, but 5% seems safe-ish.  What formula can I use to figure out my FIRE date?  Thanks so much!!!

 

[dandarc]

In excel or google sheets, the formula would be:

=NPER(.05, -7000*12, -420000, 1300000)

[dandarc]

The actual math formula is this:

FV = Future Value (1.3M)
PV = Present Value (420K)
P = payment (7000*12)
r = rate of return (.05)
n = number of periods

n = log((FV + P / r)/(PV + P/r))/log(1 + r)