You mention only two debts, mortgage and student loan, but you mention $19K in savings, which suggests that you are a saver, and likely do not have other debts.
You did not mention your (net) income and expenses (income statement), but since you have substantial savings, you likely live within your means (income > expenses). Since you mention $38K in retirement, we might conclude you are regularly saving for retirement (are you saving 10% toward retirement)?
You did not mention any medical condition or other debts, that might require a large savings, so I would suggest having 6 months savings ($2.5K x 6 = $15K) but should your net expenses be less, you might reduce this ($2K x 6 = $12K).
You do not mention any investment you might want to make, but since you did not mention any candidate investments, we can assume you have no (specific) investments you find particularly attractive. You did not mention anything you were saving to purchase that you might want to purchase.
You have combined $19K + $50K = $69K savings, and $15K would be a comfortable emergency savings, leaving $54K you could use to reduce mortgage or student loan debt.
The mortgage debt interest @4.5%, is higher, so paying that debt off would be like earning 4.5% guaranteed return on your money, tax-free. At your income, your marginal tax rate is low enough that the mortgage interest deduction (if you do itemize) would not reduce this return much (15% if you itemize).
The student loan debt interest @2.8%, would be like earning 2.8% guaranteed return on your money, tax-free.
Clearly the higher return on your 'investment' in paying off debt would be reducing your mortgage balance (over 50% higher return on investment, compared to the student loan debt).
You did not mention any circumstance that might cause the student loan rate to increase, the mortgage rate to increase, nor did you mention any difficulty making both the mortgage and student loan payments, the amounts of either payment, nor the number of years remaining to pay on either.
Should you need (or desire) to reduce your payments, you could choose to payoff the student loan to eliminate one payment, and thus decrease your expenses. Or you could choose to pay down the mortgage, and refinance (or refactor) the mortgage to obtain a smaller payment. Another strategy (assuming you have had your house for 5-7 years), might be to pay the mortgage down enough to refinance into a 15 year loan, and (assuming you have a good credit score) obtain a lower (3%) rate.
But I am going to suggest you consider a blended approach. Combine the Dave Ramsey Debt Snowball approach with the reduce the interest rate approach. Take the $54K ($57K?) available (after reserving 6 months emergency fund), and split between both. You pay your mortgage down by $27K and your student loan debt down by $27K. Your blended return on investment is (2.8+4.5)/2 = 3.65%, and you have the following
- House $202K
- Savings $15K
- Roth $38K
- Mortgage $100K @4.5%
- Student Loans $2K @2.8%
The next steps would be to,
- Focus on paying off the student loan and then use the money freed from that payment to payoff your mortgage.
- Consider refinancing into a 15 year loan for the lower interest rate.
- Consider whether a slightly smaller emergency fund ($13K) and paying off the remaining student loans ($2K) would leave you with a comfortable emergency fund. (Note that if your student loans are $300/month, the additional depletion of emergency fund would be offset by the reduction in amount of emergency fund needed over 6 months).
There are two great reasons for paying off the student loan debt. One is the Dave Ramsey Debt Snowball approach which is that this is the smaller debt, and thus represents a psychological win, and the other is that student loan debt has special treatment even in bankruptcy.