The FA has set Saturday 11, May 2013 for the Final between Manchester City and Wigan.

After the conclusion of the FA Cup semifinal matches with both Wigan and Manchester City making it through to the Final. The FA has confirmed the kick- off time for the clash between Manchester City and Wigan in Wembley.
According to a

The Oldest Club Football Cup in the World.
The Oldest Club Football Cup in the World.

publication posted on the Football Association’s official website on Tuesday, the match will be played on Saturday 11th May, 2013 with the kick- off time set at 5:15pm London Time (6:15pm GMT +1.)
As an incentive to both winner and the runners- up, the FA thereby announced the sum of £1,800,000 for the cup winner and £900,000 for the runners- up. The monetary reward is to be withdrawn from the FA Cup Prize Fund as backed by the necessary legislations and acts.