On the assumption that the rate doesn't change over that period, yes, the price will halve in just over 11 years.

You can validate that by 0.94^11=0.5062982072, where 0.94 is the ratio of the price that's left after one year. Raising that to the power of eleven gives 0.506, or just over half, as the ratio of the price remaining after eleven years.

You can get the exact time needed by dividing the log of the ratio you're looking for by the log of the ratio per year, so: ln(0.5)/ln(0.96)=11.2023055836, so the cost will halve in 11.2 years.