You have 78 payments left now, assuming you haven’t made prior additional principle payments. If you sent $6,000 in, you’ll owe 24,172, which equates to 42.6 payments, at least if your interest is simple, rather than “rule of 72” interest which is heavily front loaded. Consumer companies such as Beneficial, CitiFinancial, and HFC typically use that method (rather than “normal” banks). At any rate, paying off 12.5% debt ASAP is a sound financial strategy.
If you continue paying the $566.97 payment, you will have your loan paid off June 2020 or in 6.5 years. Making a $6000 payment in January, as your January payment (not in addition to it) will knock 19 months off your loan. You will make the last payment of $380.47 on November 2018. It will in the end save you $1,044.73 in interest.
If you increase your monthly payment by $100 after making the $6,000 January 2014 payment, you will knock off 1 whole year from the loan. You will have it paid off by December 2017 rather than June 2020 if you continue making the minimum.