The price for one share of Apple Inc. was at roughly $ $1\mathrm{.}05*$ at the beginning of $2003.$ What would the share price be at the end of $2019$ assuming a return rate of $20\%$ per year?

$1$b$)$ Actually, the share price at the end of $2019$ was roughly at $ $270.--.$ Based on that number, $*$on a like$-$for$-$like basis, adjusted for any stock splits that may have occured in between what was the annual rate of return in reality $($just based on the increasing stock price, not considering any dividends that might have been paid in between$)?$

$1$c$)$ Starting from the share price end of $2019($$ $270.--),$ after how many more years of constant growth at the same return rate $($result from b$)$ would it hit a price of $ $1,000?$