An investment company has a time horizon of $3\mathrm{.}7$ years

It's portfolio is invested in $5\%4-$year annual payment coupon bonds

The portfolio has a par value of $$2$M and current yields are $5\mathrm{.}5\%$

a$.$ Is the portfolio immunized when the bonds were purchased?

Full credit requires calculations to support your answer

b$.$ Would the portfolio be immunized in year $2?$

c$.$ If the firm wanted rebalance the portfolio in year $2$ using a $1-$year

$6\%$ zero coupon bond, what proportion of the original portfolio

should it be$?$