If you don't have any active installments then an installment can help with Credit Mix. However, Credit Mix is a small factor.http://www.myfico.com/crediteducation/w ... score.aspx
I'd recommend getting products as your financial needs dictate versus for scoring purposes. Don't just obsess over scores and the cited reasons. Even with FICO 8's in the 800's I'm seeing reasons listed and I'm well above the 740-760 range where best terms are generally offered. What are you not able to accomplish with your current scores that you would with higher scores?
smithjohn wrote:So if I take some personal loans (such as the discover one) with amounts significantly lower than my combined credit card CL, would that help the scores in any meaningful way despite the HP(i.e. over 800 would be great, increasing 3 points not so much)? Would it make any difference if I pay it off sooner
You need to consider the standard factors. The HP is the least significant of them despite how people tend to obsess over them.
By opening a new credit account you will drop your AAoA (Length of Credit History). To what degree we can't tell you but can do the math yourself to see. AAoA is just like any other average. You add up the ages of the accounts and divide by the number of accounts, including the closed accounts on your report. All we can say is that generally those with more accounts that are aged will see less of a hit than those with fewer and younger accounts.
You'll only see a benefit to Credit Mix while the installment is open. Once you've paid it off you'll lose that scoring benefit.
The balance to loan ratio on an installment does factor into Amounts Owed but it does not have the same impact as revolving utilization on your revolving accounts.
There's also an impact just from having new accounts that many tend to overlook. The impact is going to depend on credit profile. Thicker/stronger profiles will see less of an impact than thinner/weaker profiles.
smithjohn wrote:because that would mean less interest payment)?
Where is interest in the pie in the link that I provided?
tl;dr -- probably not worth it. What are your current score (indicate both model & CRA) and why are you worried over them?