$11.$ Your family runs a small manufacturing company that specializes in automotive components for disabled drivers. You are tasked with finding new equipment that can increase productivity in the shop and have just struck gold. You have found a new sand blasting machine that cleans parts almost $20$ times faster than your current equipment! The cost of the machine is $$80,000$ now, but you expect it to cost about $$87,000$ by the time you are ready to buy it$.$ You convince your family to place $$20,000$ annually in an account earning $6\%.$ How many years until you are ready to buy your new sand blaster?