I did a slightly different formula that works out pretty close to the one Arebelspy did. Mine is:
(Age-20)^1.4*Income*Factor=Expected NW
The factor varies as follows:
Under Accumulator of Wealth (UAW) = 0.05
Average Accumulator of Wealth (AAW) = 0.1
Prodigious Accumulator of Wealth (PAW) = 0.2
Mustachian Accumulator of Wealth (MAW) = 0.4
I had already created it and was tweaking the exponents and factors when I saw the one Arebelspy created. Just like with his, it assumes you start accumulating at age 20 which is a decent approximation. Some people start earlier. If you get more education, you might start later but that "should" boost your income and make it easier to save.
If you want to tweak the formula, increasing the 1.4 makes the exponential effect larger (like assuming more gains from your investments). Obviously, the starting age or the factors can be tweaked as well.
Some Examples are below:
Age 30 Income $80,000
Factor NW
UAW 0.05 $100,475.46
AAW 0.1 $200,950.91
PAW 0.2 $401,901.83
MAW 0.4 $803,803.66
Age 40 Income $100,000
Factor NW
UAW 0.05 $331,445.40
AAW 0.1 $662,890.80
PAW 0.2 $1,325,781.61
MAW 0.4 $2,651,563.21
Age 50 Income $100,000
Factor NW
UAW 0.05 $584,708.98
AAW 0.1 $1,169,417.95
PAW 0.2 $2,338,835.90
MAW 0.4 $4,677,671.81
Age 60 Income $100,000
Factor NW
UAW 0.05 $874,689.66
AAW 0.1 $1,749,379.32
PAW 0.2 $3,498,758.64
MAW 0.4 $6,997,517.27