Dirk Ward borrowed $$12,000\mathrm{.}00$ for investment purposes on May $7$ on a demand note providing for a variable rate of interest and payment of any accrued interest on December $31.$ He paid $$800$ on June $13,$$$150$ on September $10,$ and $$1000$ on November $11.$ How much is the accrued interest on December $31$ if the rate of interest was $8\%$ on May $7,8\mathrm{.}4\%$ effective August $1,$ and $8\mathrm{.}9\%$ effective November $1?$

The accrued interest on December $31$ is $

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