Suppose we have two zero$-$coupon $($discount$)$ bond $($$$1000$ face value$)$ with remaining time of $1$ year and $4$ year as the liabilities. Hypothetically how can we form a bullet strategy to immunize against the interest rate risk? Assume the yield curve is $3\%$ flat.

a$.$ purchase $1\mathrm{.}12$ share of $2-$year discount bond and $0\mathrm{.}88$ share of $3-$year discount bond

b$.$ purchase $0\mathrm{.}88$ share of $2-$year discount bond and $1\mathrm{.}12$ share of $3-$year discount bond

c$.$ purchase $0\mathrm{.}95$ share of $2-$year discount bond and $1\mathrm{.}05$ share of $3-$year discount bond

d$.$ purchase $1\mathrm{.}05$ share of $2-$year discount bond and $0\mathrm{.}95$ share of $3-$year discount bond

e$.$ We cannot form any bullet portfolio strategy to immunize the interest rate risk in this case

$8).$ explain