Ouch, that is a lot of debt. Personally, I think it's reasonable for someone making $300K+ annually to gear their budget toward wealth-building. To not do so seems like a waste of an opportunity.
First, there were a couple things about the expenses that made me do a double take.
#1 What is included under "non-medmal insurance?" Would be interested to see an itemized breakdown. You mentioned getting good full benefits from your employer... so $7K annually on insurances (not including medical malpractice) seems high, but it depends on what all you have in there.
#2 $7.5K annual cash savings is listed as an "expense." Don't mean to be too hard on you, but savings should not be accounted for as an expense.
#3 $12K annually on food seems rich for a family of two. I guess if you live in an expensive city and neither of you cook then it might be justified, but otherwise consider clamping down on that somehow. Maybe cut out the alcohol (if applicable; not a popular suggestion I'm sure)? I would think a house of two would be able to eat well spending about half that on food.
#4 I agree with BorntobeDO - the car payment needs to be gone.
The car payment is interest free and only has like 18 payments left, so I didn't plan on paying that off just for the sake of clearing it off the table.
"Clearing the table" would by my #1 priority if I were in your shoes. Only having 18 payments left gives me more of a reason to pay it off ASAP, not less of a reason. I hate payments of all kinds, but car payments are the cystic acne of personal finance (compared to reasonable mortgages, which are more like beauty marks (see Cindy Crawford)). I prefer a blemish-free face, but if you need to have something wrong, a beauty mark is the way to go. I'm going to let you in on a secret I learned from a veteran car salesman... zero percent interest is a gimmick used to sell cars. I know. Shocking, right? It's like tossing a few pennies at the customer to make them feel like they're the winner in the transaction. And some unsolicited advice about buying cars... You may be doing this already, but for anyone else reading perhaps this basic tip will be helpful. Car tip #1: You can save a lot of money by avoiding new cars like the plague... at least until actual wealth is achieved. In the meantime, buy a used car (about 3-4 years old seems to be the sweet spot depreciation-wise) with low miles... and pay with cash. If you can't afford to pay with cash, then you can't afford it. Loans seem harmless, normal, and even safe. Don't be fooled. They're a trap. Why are car loans so bad? Because they allow you to spend more than you have on an item that is proven to lose value over time (i.e. on a liability). Car tip #2: Private sellers are more likely to cave and give in to a lowball offer. Car dealers are like psychologists. They know how to maximize profit on the sale while simultaneously making you feel like the winner in the negotiation. A car buying negotiation is actually a great example of why debt should be eliminated/avoided as a general rule going forward. When doing a deal, such as buying a car, we give the associated debt a fun name by calling it "financing."
Car salesman: "Would you like to assume some debt to buy this car?"
Customer: "No thanks!"
Car Salesman: "Okay, then how about some financing?"
Customer: "Sure! That sounds smart."
Now, instead of negotiating the actual price of the car, the salesman gets to play a game of smoke and mirrors with the customer. And so the focus of the discussion shifts to monthly payments, interest rates, and loan terms. If the salesman can't "make the numbers work," he can always tell you that your trade-in is in worse shape than expected and shift numbers accordingly. The point is that debt turns this otherwise simple procedure into a more complex discussion with several moving parts. When paying cash, you have one focus - the final sale price of the car.
Debt has the same effect in other areas of life. It complicates things unnecessarily. In deals involving debt, you spend more time trying to understand how to use loans to your advantage than you do negotiating the final price to your advantage. It's not about being intelligent enough to handle the variables of debt; rather, it's about being disciplined enough to avoid debt.
I have watched my father do the 'rich dad' thing for almost 20 years, and yet he's not rich, and still can't retire. He invests in RE in lots of 'good debt' and yet because he doesn't have that paid off, he keeps getting in 'bad debt' the moment his business has a downturn. Debt is a behavioral not a math issue, I am convinced.
This guy had the benefit of assessing his dad's financial strategy for nearly 20 years. What did he learn? #1 "Good debt" is a misnomer (i.e. debt is bad) and #2 debt is behavioral, not a math issue. These concepts are absolutely fundamental. Keep in mind - most people accept debt as a normal part of life... and most people are broke.
I know you were probably more interested in getting objective advice involving numbers and interest rates, but you really have to subscribe to those fundamental concepts before doing anything else. Why? Because otherwise you would drown in options. If debt is on the table, you'll have much less clarity. Say I have $1,000 to buy a lawn mower. If I am staunchly anti-debt, then my options are obvious. I can buy any lawn mower that is available for $1,000 or less. Now, imagine I am open to using debt to help me get any lawn mower up to $20,000 ($1,000 down payment and up to $19,000 financed). Now, I'm going to have a back and forth with myself about what is possible and what is reasonable. Since everyone and their brother uses financing, it's certainly reasonable to buy with financing... right? I'll justify a decision to spend more than I have by weighing the safety features and my carbon footprint and how fat my dog is. Probably don't want to use the full $20,000, but middle of the road seems wise. So, I buy a nice lawn mower with some, but not all, of the bells and whistles for $10K ($1,000 down payment and $9,000 financed). I walk away feeling great because I got a sweet lawn mower with a super-low interest rate of 0.9%. What I don't realize is that not having a tough, anti-debt stance just cost me over $9K.
Step #1: Eliminate debt and never go back in (because debt is not about the math, it's about behavior).
Step #2: Build assets (i.e. invest in index funds +/- rental real estate with cash only).
All that being said, if I woke up in your shoes - this is what I would do...
Cash on-hand: $100K
*Use ~$7K to pay off car and never get another car loan again.
*Use ~$83K to reduce student loan balance from $342K down to $259K.
*Consider refinancing student loan to lower fixed interest rate, if possible. Not so you can carry the loan longer, but so you can slow the bleeding.
*Keep ~$10K on-hand for emergency fund (assuming you have good short-term disability insurance).
Income after taxes and 401(k) deduction: $200K/yr
*This is excellent!
Housing costs: $30K/yr
*Cut to $10K/yr by renting apartment while eliminating debt.
*After debt is gone, save at least 20% down payment for a house.
Utility costs: $7K/yr
*Cut in half by renting as suggested above.
Insurance costs: 7K/yr
*Look into why this is so high.
Food costs: $12K/yr
*Consider cutting these costs in half (less EtOH? Less eating out?).
Gas costs: $3K/yr
*Adjusted per last post.
Roth IRAs (backdoor): $11K/yr
*You can start doing it now if you want, or wait until your debt-free. Up to you.
Your original budget showed expenses at ~$128K/yr, leaving $72K/yr left over. In that scenario, it would take ~4+ years to aggressively eliminate student loans. If you make the suggested changes, expenses would be ~$100K, leaving $100K left over. In that scenario, it would only take ~3 years to aggressively eliminate the debt. Would emphasize the importance of avoiding a house at this time. A house is obviously expensive at face value, but they also come with a variety of unforeseen expenses... lawn mower, grill, indoor furniture, outdoor furniture, ongoing maintenance costs, etc. Would slow you down and prevent you from progressing quickly through the student loan mess.