On Carlos$$s first birthday, his parents deposited $$5,000$ into a savings account that earns a fixed rate of $4\mathrm{.}50\%$ and compounds interest annually. By Carlos$$s $20$th birthday, his account will have accumulated $?$ If Carlos$$s parents had waited until his $10$th birthday to make their initial deposit of $$5,000$ into the same account, by Carlos$$s $20$th birthday, the balance would have been

$

$.($Hint: Round your answer to the nearest cent.$)$