Information about Bonds A and B is given below. Construct a portfolio of these two bonds to match the value and duration of a $20-$year, $8\%$ coupon bond $($Face value is $$100).$ Bond is trading at par. Hint:

First calculate the duration of the bond.

Bond A: $1$ year zero coupon bond. Price$=$$$94\mathrm{.}26$ for $$100$ face value.

Bond B: $30$ year zero coupon bond. Price $$16\mathrm{.}97$ for $$100$ face value.