An automotive dealer borrowed $$8700\mathrm{.}00$ from the Bank of Montreal on a

demand note on May $9.$ Interest on the loan, calculated on the daily balance,

is charged to the dealer's current account on the $9$th of each month. The

automotive dealer made a payment of $$1600$ on July $15,$ a payment of $$4500$

on October $1,$ and repaid the balance on December $1.$ The rate of interest on

the loan on May $9$ was $5\%$ per annum. The rate was changed to $5\mathrm{.}25\%$ on

August $1$ and to $5\mathrm{.}65\%$ on October $1.$ What was the total interest cost for

the loan?