Dirk Ward borrowed $$13,000\mathrm{.}00$ for investment purposes on May $10$ on a

demand note providing for a variable rate of interest and payment of any

accrued interest on December $31.$ He paid $$700$ on June $10,$$$100$ on

September $23,$ and $$500$ on November $18.$ How much is the accrued interest

on December $31$ if the rate of interest was $8\%$ on May $10,8\mathrm{.}5\%$ effective

August $1,$ and $9\%$ effective November $1?$