John Brown lived in a family that always used the phrase $$a penny for your thoughts?$$ John works at a company with $420$ employees $($not including himself$)$ and is known for his humorous editorials on current events. One day John decided to start a work editorial e$-$mail called A Penny For My Thoughts. In the daily e$-$mail $($he even sent them on weekends and holidays$),$ John sent out his editorial comment for the day and simply asked that his co$-$workers repay him for his thoughts at the going rate of one penny per person. In other news, John is trying to save up money for a $10\%$ downpayment to buy a new $$160,000$ house. John banks where he can get a $12\%$ rate of return and even daily compounding of interest. If John invests his $$Penny for My Thoughts$$ earnings each day, how many years would it take for him to come up with his downpayment?