As long as we're heading down the road of debts to pay off vs not, you should also consider if paying off certain debts will hurt your credit score. I think diversity of loan types might be a factor on credit score - but don't quote me. It's worth researching a little, since your credit score will be extremely important in getting a home loan.
Consider investing vs loans as a choice: would you rather earn 2% or earn the stock market return?
A loan of $10,000 at 2% is like being drained of -2% while keeping $10,000 to invest. Historically the stock market does much better than 2% (but there's no certainty about stock performance in a particular year), so investing has tended to be a better choice than paying off the loan.
There's an emotional component though - the feeling of being debt free might be worth more than the earnings on that money in the stock market. But in terms of a profit decision, the stock market is likely to beat 2%, and so be a better place for money than paying off the loan.
And again, take a look at how paying off debts impacts credit score - not sure, but it's worth working on your credit score to increase it into the top range (760+? 800+?) before the house purchase.
As far as I know with regards to credit score, the only component that really matters, with regard to open and closed loans, is length of credit history. If you close all your loans out you can wind up in a situation where you essentially have no credit history, which is bad and hurts one component of your score.
Generally the difference between someone with 800+ and mid to high 700's is length of credit history. A credit card is the easiest to keep for improving your age score since this is the only loan you can keep open indefinitely without inuring interest charges.
Most online credit score estimates falsely drop off your closed loans instantly from your credit history. Depending on the credit score system a closed loan in good standing can positively impact your score for 7-10 years. All my personal student loans for instance are now closed over the last 2 years. When I get a score from a company it tends to be 780ish. But my FICO always estimates at 750-760. The only difference is the credit score the companies pull has my student loans still factored into my credit history. While the FICO killed them off.
In general for credit it is prudent to keep a credit card with a utilization avg somewhere around 10 percent. That way you always have a credit history. Beyond that I wouldn't worry about artificially keeping loans open. By the time one drops off your record you could likely have built up a new age score based off a credit card.
As far as the difference between 760 and 800+ for getting a home. I can't imagine it is huge, but maybe it matters. Probably depends on the lender.
I think the emotional part of not having any small debt will eventually get the better of me. But in general the utility of having $16k in cash versus paying off low interest debt is much higher.
The car loan, I know its not very mustachian, is 1.75% interest. I could easily stick pay off money in a 5 year CD at 2.3% and do better than paying it off. The student loan is 2.6% so a bit worse but still somewhat trivial given it is a small amount of debt.
My plan as of now is to just sock away the case in the Capital one money market and I will reevaluate if I want to kill a loan as each year rolls buy. As some have noted odds are I can find a more productive use for the cash than paying off the loan.