How I calculated When We Will Reach Zero Net Worth

We have a lot of student debt. Our net worth is deeply in the negative. Making it up to a zero net worth is an important psychological milestone for us, and I wanted to figure out how to calculate the date we’d reach this milestone.

Google wasn’t able to help me with this one, so I accepted the challenge to come up with a calculation myself. There are several calculators out there to help figure out how long it will take to pay off debt or how to save to reach a target amount, but surprisingly nothing came up to calculate zero net worth for people who are simultaneously saving for retirement and paying off large amounts of student loan debt. I started with a little help from the classic train problem, but that made it more complicated than it needed to be.

Two Trains

I thought that calculating when we will reach zero net worth was essentially the classic math problem of two trains traveling towards each other at different speeds and calculating when and where they will meet. The trains are vectors going in different directions so the calculation is done using the relative speed (or relative savings in my case). Since we are paying off debt and saving for retirement, both vectors are going in the positive direction. I’m a little embarrassed to say I didn’t figure all this out until I tried solving the problem both ways and found it was going to take longer to reach zero net worth than it was to pay off our loans. Obviously I did something wrong so I sent the trains on their ways and started over.

First, take a deep dive

In mid-March we sat down and seriously reviewed where our money goes every month, because we were unhappy with how slowly our debt was going away. As a result, we temporarily stopped fully maxing our retirement contributions and pulled back to just get the employer match, so we can plow every spare dollar into student loans which are at 4.5% interest, and climbing. As a result, we’ve increased our monthly loan payments by 10%. I used these more recent funds distributions, including employers 50% match for our 403(b), in the calculation rather than an average of the last 4 months. 

Net Worth 101

To start, I figured out our net worth (assets minus debt). We don’t have a mortgage and don’t carry credit card debt (we use credit cards for all our spending, but pay it off in full every month), so our only debt is our student loans. Our assets include retirement savings (403(b), 457(b), and Roth IRA for each of us), a 529 for each of our children, and our savings accounts (an emergency fund and an account for medium-term goals).

There were a few lessons I learned from trying to reach net zero full speed ahead. One, I was not interested in the distance between our debt and assets, but our distance to zero. Rather than starting with our debt or assets I needed to start with our current net worth. Two, paying off debt and contributing to savings are vectors going in the same direction, so I needed to add them.

Time to zero net worth

I plugged in some numbers, and the results seemed plausible. So here’s the equation I came up with

Using our net worth when Paradox Wealth was born and our current rate (without interest) our calculation looks like this

Doing this calculation with negative net worth gives us a negative time to zero net worth. To simplify things, I just dropped the negative sign. Our time to zero net worth is 32.65 months, or 2.72 years. We will reach zero net worth around late December 2020, assuming we maintain our current loan payments.

What is not accounted for

An important note is the simple problem of two trains traveling at constant speeds doesn’t take into account slowing around turns or additional stops. The equation I came up with is oversimplified, it doesn’t take into account interest or returns earned on our investment portfolio. If you have the math expertise, please share your knowledge and help me  improve the equation.

 

When do you expect to reach zero net worth? If you’ve already made it, what did you do to celebrate?

 

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