You are constructing a portfolio to immunize a $$17\mathrm{.}0$ million cash flow that occurs four years from today. You have a bond $($X$)$ with a duration of $2\mathrm{.}65$ and a quoted price of $96\mathrm{.}142$ and a bond $($Y$)$ with a duration of $6\mathrm{.}36$ and a quoted price of $106\mathrm{.}880.$ The YTM is $5\mathrm{.}0\%$ on all bonds. Assume that all bonds pay annual coupons and have par values of $$1,000.$ Assume that P$/$E ratios are computed using current price and expected earnings $($rather than current earnings$),$ and that all earnings and dividend values are annual values.

a$.$ What will be the value today of your immunization portfolio?

b$.$ What will be the weights of the two bonds in the immunization portfolio?

c$.$ How many X bonds would be in the portfolio?