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FSA (Flexible Spending Account) Savings

An FSA is a tax-advanted account that allows you to put away pre-tax money to be spent on qualified health care costs. This is usually deducted from your paycheck by your employer.

There are some of the downsides of FSA, one being that money put aside for a year must be spent, or else it is forfeited up to a roll-over amount unique to each plan. FSAs also are restricted as to what they can be spent on, with some plans (like my LPFSA) only allowing dental and vision expenses.

The most interesting question to me is just how much are you saving by using an FSA?

Doing the math

Well, obviously you are saving on taxes. With an FSA, you are putting away money before federal (and usually local) taxes are withheld. This is unique to everyone, but calculators like this will give you your effective tax rate, which we can call $T$.

• For example, someone in Chicago making $\$100,000$ has an effective total tax rate of 26.3% or $T=.263$

Now lets say you have a procedure/medication which you paid using your FSA. Let’s denote this as $C_\mathrm{FSA}$.

We see the following is true with $I$ being the money you make, your income, before taxes are applied:

$$I(1-T) = C_\mathrm{FSA}$$

Thus,

$$I = \frac{C_\mathrm{FSA}}{(1-T)}$$

• Lets say the person in Chicago spent $\$200$ on their doctor visit and uses their FSA: $C_\mathrm{FSA} = \$200$
• We see that with taxes, $I = \$271.37$, so they would’ve had to make $\$271$ dollars to pay for this visit instead of $\$200$!
  • $I = \frac{\$200}{(1-.263)} = \$271.37$

Obviously one way to look at this is savings $S$ - how much money did we save on taxes by paying using an FSA?

$$\mathrm{Savings} = S = I - C_\mathrm{FSA}$$ $$S = \frac{C_\mathrm{FSA}}{(1-T)} - C_\mathrm{FSA} \tag{1}$$

• Again, for the visit we see that we’ve saved $\$71.37 = \$271.37 - \$200$

Dividing savings by the cost of something using the FSA, we can get the FSA Savings Rate $R_\mathrm{FSA}$. So for all things we use our FSA for,

$$R_\mathrm{FSA} = \frac{S}{C_\mathrm{FSA}} = \frac{1}{(1-T)} - 1 = \frac{T}{(1-T)} \tag{2}$$

• Our friend in Chicago would save 35.68% on everything billed to their FSA!
  • $R_\mathrm{FSA}(T) = \frac{1}{(1-.263)} - 1 = .3568$

Savings are tax dependent

The important thing to note here is that this savings rate is solely dependent on your effective tax rate $T$. Again available with calculators.. Clearly, it is also non-linear.

As with all tax-defferal mechanisms, FSAs are most effective for those with higher tax rates (and higher incomes). If your tax was 50%, $R_\mathrm{FSA} = 1$, meaning that you’d save 100% the price of an item using an FSA.

Still even at lower tax brackets, where you might be paying 20% in taxes, FSAs can save you 25%. If you had nearly maxed your FSA with $\$3,000$ and used it all, thats $\$750$ in savings.

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Below is $(2)$ graphed, showing savings rate $R_\mathrm{FSA}$ vs. Tax Rate $T$.