Your emergency fund seems on the high side to me (about your age, similar income, similar cost of living city). I try to aim for $5k or so, which is about 2.5 months of expenses, but my job is pretty stable and I have safety nets (employable spouse, home equity, lots of credit, family who would give me the shirt off their backs). It's a personal comfort thing, so you do you.
Here's how I would approach it in my brain, if it were me.
Current Situation:
Monthly gross (and taxable income): ~10400
Taxes/other paycheck reducers: ~3600 (about a 34% tax rate)
Monthly net: 6800
Fixed expenses: 1500
Minimum Loan Payment: 3500
Total left over: $1800
Now, if you max out a 401(k), you would end up with this scenario:
Monthly gross: 10400
401(k): 1500
Taxable income: 8900
Taxes (assuming same high rate, which might not be accurate): 3026
Monthly net: 5874
Fixed expenses: 1500
Minimum Payment: 3500
Total left over: $874
You can then take that $874 and either 1) throw it at your student loans, or 2) fully fund a Roth IRA, which you are now eligible for because you've reduced your adjusted gross income to be under $116k. You only need $458 and change per month to fully fund a Roth IRA. So, you still have $416 to throw at your student loans. Plug this into an online calculator to figure out how much this will save you in interest. I've plugged your numbers (assuming some dates, check your details) into the bankrate one, and estimated that you'd save a total of $15k in interest and shaved about 1.5 years off of your student loan.
At the end of this scenario, you have:
1. A fully funded 401(k), beginning the magic of compounding interest working in your favor while you're younger
2. A fully funded Roth IRA, which but for #1 you would not be eligible for, also with compounding interest
3. A savings of $15,000 in student loan interest
4. A reduction in your tax liability to the tune of $574/mo, or $6888 per year.
By October 2024, you will have:
1. $162,000 in contributions to your 401(k), plus all of the growth your fund has experienced in that time (details may vary based on fees on funds your employer offers, market, etc.).
2. $49500 in a Roth IRA, plus 2% reinvested dividends (if you use VTSAX), plus all of the growth
3. A paid-off student loan
4. Savings of 15,000 in student loan interest
5. Savings of $61,992 in taxes
Now, compare the scenario of paying down your student loans instead.
1. Shaves about 4 years off of your student loans, meaning you'd be ready to start saving for retirement in 2022, at age 38. That might stress me out.
2. Saves about $55,000 in student loan interest
By February 2022, you will have
1. A paid off student loan
2. A savings of $55,000 in student loan interest
3. Higher tax liability than you would have otherwise, and
4. No retirement savings, when you're nearing 40.
Please check my math, your pay stubs, and your student loan amortization schedule. There are certainly a lot of variables in play I didn't account for - raises, changes in employment or employment benefits, changes in your COL, changes in your tax filing status, changes in the tax code, etc. etc. But, given the information you know now, if it were me, I'd pick Scenario #1.
Steps:
1. Build emergency fund
2. Max out 401(k)
3. Max out Roth IRA
4. Throw everything left over in student loans