Suppose Patrick Goldsmith deposited $$1000$ in an account that earned simple interest at an annual rate of $10\%$ and left it there for $5$ years. At the end of the $5$ years, Patrick deposited the entire amount from that account into a new account that earned $10\%$ compounded quarterly. He left the money in this account for $5$ years. How much did he have after the $10$ years? $($Round your answer to the nearest cent.$)$

$