Best formula for calculating FIRE date?

[iheartcharts]

Based in part on the Early Retirement Calculator from Networthify, I wanted to create a formula that would provide an estimate in years of the likely FIRE date. I'll share what I've used, and would love to hear suggestions and improvements from others who might have created their own. Given the homemade nature of this, I'm betting that I've introduced a blindspot or two that someone else might see more easily than I.

What I created, simplified:
I = Investments
N = Magic number or FIRE goal
R = Current weekly savings rate
Investment growth rate = 7% per year

How I did it:
I used NPER- the number of periods for an investment based on periodic, constant payments and a constant interest rate.
Formula: =NPER(7%/52, -R, -I, N)/52

I've created an example Google Sheet here with an example.

On my own tracking document, I've added another twist - my current savings rate is the amount I've saved so far in 2015 divided by the current week number. That would be something like =Your_2015_YTD_Savings/WEEKNUM(NOW()), nested into the formula above.

Thoughts?

[ender]

I have a spreadsheet setup, where I have the following columns (everything in 2015 dollars):

• Year - obvious
• Investments - value of investments
• Contributions - new contributions/year
• Withdrawals@Percentage - withdrawals/month @ given SWR

I then have as inputs:

• Starting investment total
• After-inflation, average investment growth rate
• Withdrawal rate

It doesn't give me a perfect answer, but it easily lets me play with the inputs to see when my stash provides the right monthly outcome.

A formula will nearly never work for us because we currently have two incomes and will eventually have one (with kids, hopefully). This means our savings rate will almost assuredly decrease somewhat, with a larger initial stash. This is impossibly tricky to incorporate into a single formula.

[Cougar]

imo it doesnt matter until you spend a year or two tracking expenses. once you can live with what you're spending; then you now how much you need and just need to save until you hit that number.

any calculator will work.

[MDM]

If you'd also like to include the effect of existing assets, there's also a formula first posted in these forums (AFAIK) by Heart of Tin:
    Time in years to FI = Ln((S + i*E/WR) / (S + i*A)) / Ln(1 + i)

A = Asset amount currently invested in funds you will draw upon in retirement.
E = Total (including taxes) annual expenses in retirement
i =  Real return on invested retirement funds.
S = Annual amount invested in funds you will draw upon in retirement.
WR = Withdrawal Rate planned for retirement, using Trinity Study definitions.

Networthify  uses an equivalent form of this equation, with
“Current annual savings” = S,
“Current annual expenses” = E,
“Current portfolio value” = A,
“Annual return on investment” = i,
“Withdrawal rate” = WR.