Let's assume that an investor's portfolio includes a two$-$year bond with a nominal value of $100,000$ and an annual coupon with an issuance interest rate of $8\%.$

I. Calculate the bond's price and its interest rate risk $($duration$)$ if the yield at maturity is $9\%.(2$ points$)$

II$.$ Calculate the bond's duration and, based on this measure, determine the bond's price if interest rates increase by $0\mathrm{.}001.(1$ point$)$

B$.$ Let's assume that an investor in a specific sector with a required annual return of $12\%$ evaluates two stocks in the sector as they are interested in investing their capital in one of the two stocks:

Stock A: Current annual dividend of $1\mathrm{.}50$ and expected annual growth of $8\%.$

Stock B: Current annual dividend of $2\mathrm{.}25$ and expected annual growth of $7\%.$

If the price of Stock A is $35$ while that of Stock B is $50,$ which stock would you recommend to the investor and why?