Noah wants to buy a $5$ year annuity. He has two options.

Option A pays $$1000$ at the end of each year, starting one year from now. It earns interest at $6\mathrm{.}25\%$ compounded annually.

Option B pays $$500$ at the end of every six months, starting six months from now. It earns interest at $6\mathrm{.}25\%$ compounded semi$-$annually.

Which annuity should Noah choose? Write an explanation that includes calculations to support your answer.