Three years ago Los Pollos Hermanos $($LPH$)$ issued a high$-$yield bond with a coupon rate of $14\%,$ paying semiannual coupons. When originally issued the bond was sold at par and had five years until maturity. Currently, LPH

bonds have a yield$-$to$-$maturity of $16\%,$ and the next coupon payment is in $6$ month from today. By how much is the

duration of LPH bonds higher than that of an AAA rated zero$-$coupon bond with an interest rate of $9\%($APR$,$

annually compounded$)$ and $18$ months until maturity? Note, report a negative number if LPH has the lower duration

of the two bonds.