It's math. Math works at every end of the spectrum, and it's as accurate as your assumptions are.

Now rerun your method with *that* savings, and let me know what answer you get, and if you think my estimate of 49 years is "waaaay off the mark." ;)

EDIT 2: If I run my calculation with 12.2k annual contributions (though that's impossible based on the numbers OP provided, but to test the time to FI under saving 12.2k, I changed their gross from 51.6k to 56200, which minus their 44k spending is 12.2k annual savings), I get a time to FI of 39 years, 1 month.

I agree it's math, and I love math, and math will always give you the same answer based on the equation or model you are using. My issue isn't with your math, but with the model itself.

FYI, here's how I arrived at my above calculations (I'm showing my work!)

Based on the OP's information,

starting balance: $20,000

Yearly contributions: $12,200

Assuming a return of 7% per year (yes, returns will fluctuate):

F = D( ( (1 + r/n)nt – 1) / (r/n) ) + B(1 + r/n)nt

&

a return of 7%

F = $1,125,000 (from 4% SWR of $45k annually)

r = 0.07 (an estimate from historical returns after inflation, dividends reinvested)

B = $20,000 (from OP's numbers)

at 28 years, 9 months said account will be worth: $1,257,868, setting ups a 4% SWR of just over $45k.

The equation itself is in an excel spreadsheet.

I agree that some of the numbers from the OP don't add up. But what's different about your two calculations is that I'm running this solely on the amount saved each year, and not bothering with savings rate as a percentage of income.

Did I screw up anywhere?