# Savings Rate Challenges

To increase you ravings rate by 5% via salary increase, you need…

c = current savings rate

i = savings rate increase

e1 = current expenses

e2 = target expenses

t1 = current take home pay

t2 = target take home pay

1.  The percentage you spend is your current expenses divded by your take home pay.

e1 / t1

2.  Your current savings rate is 100% minus the percentage you spend.

1 – e1 / t1 = c

3.  Solve for e1

e1 = t1 * (1-c)

4.  Your new savings rate is 5% high and is equal to 100% minus the percentage you spend.

1 – e2 / t2 = c + i

4. Since we aren’t spending any less money, e1 === e2

1 – e1 / t2 = c + i

5.  Substitute e1

1 – [t1 * (1 – c)] / t2 = c + i

6.  Solve for t2

[t1 * (1 – c)] / t2 = 1 – (c + i)

t2 = [t1 * (1 – c)] /  1 – (c + i)

7.  Each take home pay corresponds to a gross income.  We can write this

t2(g2) = ?

t1(g1) = ?

The ? will be a function that computes t2 using g2 and the federal and state tax tables.  I am too lazy to write it out, so instead I used a take home pay calculator to compute gross income in \$5k increments.  I only solved it up to \$180k in salary b/c that resulted in an increase to \$400k at the highest 90% -> 95%  savings change, and I think salaries above \$250k are just stupid b/c they are taxed to death.

My final output is a graph of what new salary you need in order to effect a 5% increase in savings, based on you current salary and current savings rate.

What we see from this is that for people starting out at a low savings rate w/ a normal American income below \$100k, a <\$5k salary bump will get you 5% savings instantly.  Whereas higher income people trying to get from 90% to 95% have a hell of a time, often having to get salary bumps of \$100k or more.

Here is another view.  Each color represents another \$50k range of salary, but I give up at \$400k, so anything above \$400k just reads as \$400k.

The chart of Savings Rate Punishment (TM).  I replaced the savings percentiles with the years a person has to work in order to retire.  For me, for example, my savings rate right now can be around 75% (based on spending \$2k/month).  That means I need to work at least 7 more years (according to the assumptions here http://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement/).

Starting from scratch, if I want to level up to six years, I need to find a job paying \$190k.  That’s possible, but very difficult, especially since I don’t have a PhD or years of management experience / MBA.  If I want to level up to 4 years, I’ll need to earn \$265k.  Not very many software jobs pay \$265k.  If I want that salary as an engineer, I either need to get into finance or get a PhD (which, of course, would be very wasteful b/c it would take 5 years to complete).  At a salary of \$150k, people with savings rates 60%  or below only need to increase salary by \$20k of less in order to level up.  This is very doable just by asking for a raise and being a solid senior engineer, especially at a large company.

For people earning \$60k or less, no matter what your savings rate, you always have a clear path to level up.  But once you get above ~\$115k in salary, leveling up really starts to get more difficult after your savings rate is 80%.
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