some thinking, you decide to start saving to finance another, cheaper machine which costs $2$ million. More precisely, you deposit $240,000$ on the company's savings account, at the end of each year. The annual interest rate is $6\%.$

After how many years will you first be able to purchase the new, cheaper machine?

After $12$ years

After $11$ years

After $14$ years

After $13$ years

After $10$ years