Today is $2021-11-17.$ Dayo buys a T$-$bill with a face value of $$15,000$ that matures on $2022-02-11.$ The annual simple

interest rate is $2\mathrm{.}300\%$ and the daycount convention is ACT $/365.$

a$)$ How much does the T$-$bill cost?

b$)$ The interest rate changes, so on $2021-12-17,$ Dayo sells the T$-$bill to Man$-$Duen for $$14,965\mathrm{.}56.$ What is the new

annual simple interest rate $?$

c$)$ The interest rate doesn't change again, and Man$-$Duen wants to sell the T$-$bill on the first day they can get more

than $$14,982\mathrm{.}78$ for it$.$ What day does Man$-$Duen sell the T$-$bill, and what price does he receive?