I'd agree with the earlier poster who suggested writing letters asking for a goodwill removal of the lates reporting on the loan, but keep in mind while negotiating that if you shorten the term of the original loan, you aren't helping the bank - you're actually hurting them in the only place they really care about, their own pockets, because you are shortening the term and thereby lowering the amount of interest you will pay them overall. Does it make good sense from the comsumer (your) side to pay it off ahead of time and eliminate interest where possible? Absolutely. Does it entice them to do something they are hesitating to do? Not really.
Pay for delete is a tactic that seems to work sometimes when people are dealing with closed/charged-off debts that the original creditor (or current collection agency) doesn't expect to ever be paid. In these cases, offering them a payment on at least part of that debt in exchange for their deleting their reporting of it interests them, again because they didn't expect ever to collect anything on it. With open accounts, for which they are still going to receive the regular expected payments and the account activity (in the case of a credit card,which generates fees paid to them by the merchants), it is a less interesting proposition to them. They are not supposed to report falsely, after all, and they cannot simply delete the entire tradeline because the account is still open and active.
If you have some extra cash on hand, you might want to see about opening a secured credit card to help with your file and with your overall utilization (if you open a $500 secured card, for example, and then don't use it your utilization will be $150 out of $1000, or 15%, rather than $150 out of $500, which is 30%).
