Want to earn up to $20 back for not using all of your plan minutes from your wireless carrier? Well, perhaps it’s time to look into the newly launching Cox plan that does just that. Reuters is running a story right now about the intrepid new offering,

After a year of testing, Atlanta-based Cox opens its mobile phone service to the public on Friday with an aim to winning customers from AT&T Inc and Verizon Communications – its current competitors in video, home phone and Internet service.

As Verizon and AT&T have entered the pay-television market, Cox and its cable counterparts have been fighting back with telecom services such as wireless. Cable firms Comcast Corp and Time Warner Inc offer wireless via their Clearwire Corp venture with Sprint Nextel.

The new Cox service starts at 450 minutes a month at a schedule of $40. This is rather comparable to their competitors—however, what makes them every different is that Cox is offering a money back bounty for unused minutes at a rate of about 5 cents per unused minute and there’s a $20 cap a month for family plan customers.

The first offer of its kind, the Cox gambit gives a lot more value to a customer’s minutes than any other plan. The only one that even comes close happens to be AT&T rollover minutes plan which allows customers to add a certain number of unused minutes from one month to the next; the price point for AT&T, of course, is that the customer is unlikely to use all of the extra minutes and thus won’t be able to get their full value.

Competition will be stiff, Cox may be a telecommunications company but they’re a cable company from the beginning.

The cash-back offer will probably appeal more to the penny pinchers in this grinding economy and it may yet nab customers from Verizon Wireless and AT&T who see a strong value in actually getting a reprieve for their unused minutes rather than letting them pile up and then evaporate.