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Mix of credit doesn't account for much points. It's really just something they use to get you to apply for things you don't need.
If you need an SSL for an extra 20-30 points then go for it but, otherwise it's not a big deal.
Don't take the hit to make the marketing people happy.
Closed loans still count for the purposes of credit mix. Open loans seem to be scored more favorably than closed because like the revolving portion of your score, you are scored on how you are currently managing your accounts, not what you have done in the past(assuming it is closed in good standing).
It is common for people to lose points when they pay off their only open installment loan. The answer is a little more complex than that though. If you just get a new loan, you are essentially at 100% utilization. As time goes by and the amount you owe compared to what you borrowed decreases, you scores should improve gradually. When most people pay off a loan, they are closing an active account with ideal utilization for scoring purposes. While this may be great that you have successfully paid off something like a car, it probably won't be so great from a scoring perspective..
The 20-30 point scoring boost only kicks in when you are under 8.9% of the original loan. Since you already have installment accounts on your report, credit mix is satisfied, so you would actually lose points for opening a Self Lender account.
What you really want to do is find a loan like an SSL that you can pay down to <8.9% and have it push your next due date out many years. That will give you a solid boost that will last until you pay off the loan whereas Self Lender will only give you that boost for a month or two at the very end of the loan.
I opened a SSL with Navy Federal and got a 20-30 point boost across the board once the SSL reported it was paid down to 8.9% and it has remained for a few months now. That was worth it since it's a 60 month term. I had closed and paid student loans and a closed and paid personal loan on my reports and got that scoring boost.