Brand New Sentence

Let's do the math on this then. TL;DR: comes out to 22% annual savings rate, maybe 15% with market returns factored in.

So we'll have four variables:

s: starting salary

r: raise coefficient per year, eg. 1.05 would be a 5 percent raise per year

v: retirement savings rate, eg. 0.05 is saving 5 percent a year including employer match if you can get it

n: number of years working

So the amount saved would be the savings rate times starting salary for the first year, plus the savings rate times the starting salary times the raise coefficient for the second year plus the savings rate times the starting salary times the raise coefficient squared ...

Which is:

(sv) + (svr) + (svr^2) ... (svr^n)

We can extract out the sv to make it:

(sv)(r+r^2...r^11)

The second part is the sum of the geometric series which is also:

(r^(n+1)-1)/(r-1)

So all in all we get

(sv(r^(n+1)-1))/(r-1) = Retirement savings

If we want 2 times salary at the end then we get

(sv(r^(n+1)-1))/(r-1) = 2sr^n

The s's cancel out so we get:

(v(r^(n+1)-1))/(r-1) = 2r^n

So let's plug in some numbers we'll say:

r = 1.05 = 5 percent raise a year

n = 11 = working for 12 years from 23 -> 35, don't count the first year

So:

(v(1.05^(11+1)-1))/(1.05-1) = 2*1.05^11

15.91v = 3.58

v=0.225

Or you'll need a savings rate of 22% ... which seems absurd. If you get no raises then it gets lower as your end salary is lower so it becomes a simple 12sv=2s or 1/6 , 17%.

Someone please correct me if I'm wrong, haven't done math like this in a while. Yes there should be market returns factored into this, I don't feel like doing that math but claude says that it would be about 15% if you factor that in.