Suppose a bond manager wants to restructure his portfolio with duration of $2\mathrm{.}97$ such that its duration is $90\%$ of that of the fund's benchmark, which is $3\mathrm{.}68.$ The manager plans

to use $5-$year Treasury note futures contracts that have a dollar duration of $$5,022.$ If the manager's portfolio has a market value of $$48,109,810,$ how many futures contracts

should he buy?

$66$

$11$

$99$

$33$