$11.$ Assume an investor has a price objective of $$10,000$ for a $90-$day Treasury bill with a face value of $$10,000$ and a current market yield of $2\%.$ The investor plans to hold the bill until maturity and has a desired rate of return of $2\mathrm{.}5\%.$

a$)$ What is the purchase price of the Treasury bill that would allow the investor to achieve their price objective?

b$)$ If interest rates rise by $0\mathrm{.}5\%$ before the Treasury bill matures, what is the potential loss in price and yield for the investor?