A demand loan of $$3000\mathrm{.}00$ is repaid by payments of $$1500\mathrm{.}00$ after two years, $$1500\mathrm{.}00$ after four years, and a final payment after eight years. Interest is $9\%$ compounded semi$-$annually for the first two years, $10\%$ compounded annually for the next two years, and $10\%$ compounded semi$-$annually thereafter. What is the size of the final payment?

The final payment is $

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.$)$