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Hello Sassy. If you pay off your student loans, that will not affect your AAoA. FICO considers both closed and open accounts in computing one's AAoA, therefore an account going from open to closed has no effect -- whether we are talking about immediate effect, or even an effect 7-8 years down the road. Eventually the closed accounts will fall off your reports in ten years, but that is way way down the road.
That said, paying off all your open installment accounts will indeed harm your FICO 8 score, though by how much we can't guess unless you tell us the original amount of the loan and the current amount owed (for each loan).
As you can see, simulators often given flat out false information that can lead people to attempt expensive strategies that harm their score. Glad you are asking us first.
PS. Mortgage scores are hurt less by installment loan payoffs, but they are certainly not helped.
Hi Sassy. When is your best guess as to when you would buy a house?
Are those student loan lates the only derogs that you have on your report? No other lates, collections, chargeoffs, liens, etc?
The best thing you could be do to prepare for your home purchase is getting those late payment marks on your report removed. That is not a slam dunk, but you have a shot at being able to convince your lender to do that. Keep making perfect payments and keep the loans open so that you have some leverage. People like Brutal Body Shots and many others know a lot about how to do that.