Not sure on cost but running at 24 hours a day, 365 days a year it should last about 4.5 years. But most warranties are 3 years for a reason so pry closer to 3.5-4 years.
Backlights usually have a pretty long half life. There was a graph that I saw online that showed how the brightness was affected. After like the first 100 hour of use, you've basically lost like 30% of your brightness. But beyond that point, you can use it for hundreds of thousands of hours before you reach the 50% mark. And since you probably won't even be running your LCD at 100% brightness in the first place, by the time half the brightness is gone, you can just crank the brightness up to make up for the lost brightness.