Cold Duck Manufacturing Inc. buys on terms of $\frac{2}{15},$ net $60$ from its chief supplier.

If Cold Duck receives an invoice for $$1,545\mathrm{.}78,$ what would be the true price of this invoice? $($Note: Round all intermediate calculations to four decimal places, and your final answer to two decimal places.$)$

$$1,136\mathrm{.}15$

$$1,287\mathrm{.}63$

$$1,514\mathrm{.}86$

$$1,590\mathrm{.}60$

The nominal annual cost of the trade credit extended by the supplier is $q,$ assuming a $365-$day year. $($Note: Round all intermediate calculations to four decimal places, and your final answer to two decimal places.$)$

Suppose Cold Duck does not take advantage of the discount and then chooses to pay its supplier late$-$so that on average, Cold Duck will pay its supplier on the $65$ th day after the sale. As a result, Cold Duck can decrease$-$its nominal cost of trade credit by $$ by paying late. $($Note: Round all intermediate calculations to four decimal places, and your final answer to two decimal places.$)$