Question $13$

Calima Financial would like to perform a duration hedge to reduce the interest rate risk exposure of their fixed income portfolio. One of the assets they are considering for the hedge is a $20$ year floating rate bond that makes semiannual coupons which are tied to LIBOR. Find the modified duration of this bond if it has a face value of $$4,000$ and it just paid a coupon today. The current LIBOR curve is shown below.

Make the following assumptions if necessary, $(1)$ use a change in the interest rate of $0\mathrm{.}0001$ for any computations $(2)$ the LIBOR curve is flat after $1\mathrm{.}5$ years. Remember, MoD is a positive number.