Assume that an investor has a price objective of $$1,005,000$ for a $180-$day commercial paper with a face value of $$1,000,000$ and a current market yield of $2\mathrm{.}2\%.$ The investor plans to hold the commercial paper until maturity and has a desired rate of return of $2\mathrm{.}5\%.$

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

b$)$ If interest rates rise by $0\mathrm{.}3\%$ before the commercial paper matures, what is the potential loss in price and yield for the investor?

c$)$ If the investor's price objective changes to $$1,007,000,$ what is the new purchase price of the commercial paper assuming no change in interest rates?