A co-signed loan involves two basic agreements. The first is the co-signer's willingness to volunteer to pay the primary borrower's debt if she is unable to do so on her own. The second is between these two individuals and the lender, which improves a loan application based on the credit profiles of both. It's easier for the borrower to jettison the co-signer than vice versa, and it depends on the primary borrower's credit profile.
Refinance the Loan
If you're the primary borrower and want to remove the co-signer, you can usually do so without the co-signer's involvement if your credit is strong enough to allow you to qualify for a new loan on your own. You don't need the co-signer's permission to refinance the loan so it's solely in your name. Alternatively, you can refinance with another co-signer -- useful if you want to separate your loan from a divorced spouse, for example.
Pay it Off
An obvious way to remove a co-signer is to pay off the balance. If you don't have the cash to make that happen, a low-interest credit card can be an option, particularly if there's a small enough balance that you can pay it off before any promotional period ends. You also can get rid of the co-signer by selling the financed asset and using the proceeds to pay off the loan.
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Some loans include provisions for co-signer release after a specific period of time. Those with a cosigned Sallie Mae student loan, for example, can apply for cosigner release after graduation if they've made 12 consecutive months of on-time principal and interest payments. Other conditions include being old enough to enter into a binding contract in the borrower's state, providing proof of income, passing a credit check, and having no student loans in default and no 90-day delinquencies within the past 24 months. If you meet the required conditions, fill out the Application to Request Release of Cosigner(s).
Even with loans that automatically offer the primary borrower the opportunity to remove the co-signer -- and for the co-signer to remove herself from the obligation -- it doesn't happen automatically. You have to apply for removal as your loan agreement dictates. If you delay, and if the primary borrower misses a payment in the meantime, you may be out of luck.
If you're the co-signer looking to be taken off the loan, your options are far more limited. The contract with the lender places you on the hook for the debt, and there's little incentive for the lender to take you off the note unless there's evidence that your name was added fraudulently. You can try helping the primary borrower improve his credit score, or see about closing the account. Beyond that, your best option may be to pay off the loan as fast as possible to avoid the risk that the primary borrower will default.