One thing that I did not consider is only increasing my spending by the rate of inflation, and saving my raises. Assuming my raises outpace inflation, that could make a substaintial difference.
I'm surprised no one pointed this out. Inflating your spending, but not your savings is a pretty big mismatch. If you just inflate your savings at the same 3.5% rate, then your required return goes down to 9.7% - still pretty big.
The big benefit will come if your income goes up faster than inflation,
and you don't increase spending along with it. The italics are important, because the trap most people fall into is increasing their spending, and then you are actually falling behind your "base case" assumptions. For example, if your income goes up 5% faster than inflation, and you are able to save 1/2 of that (the other half going to taxes), then you can hit your number in 15 years with 7% investment returns.
Small changes change the numbers a lot. If you work 25 instead of 20 years, if you save 25% instead of 20%, if you can save your raises or if you end up including them in your lifestyle, if you make 6% or 10% investment returns - all these make a huge difference. Even the path of investment returns matters (high returns later is much better than high returns early in your plan). Who knows what the future will bring? Your life will change a lot over the next 20 years, and things may turn out much better or worse than you have assumed. As FIREdreamer said earlier, don't worry too much about the math. Just do what you can, keep moving in the right direction, and stay flexible.
The lesson I would take is that a 20 year working life is difficult, but not impossible, and significant savings will be necessary to make it happen.
