Dirk Ward borrowed $$13,000\mathrm{.}00$ for investment purposes on May $26$ on a demand note providing for a variable rate of interest and payment of any accrued interest on December $31.$ He paid $$1000$ on June $5,$ $$100$ on September $27,$ and $$900$ on November $24$ How much is the accrued interest on December $31$ if the rate of interest was $5\%$ on May $26,56\%$ effective August $1,$ and $585\%$ 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 sox decimal places as needed$)$