$214$ points

A trading portfolio consists of two bonds, A and B$.$ Both have modified duration of $3$ years and face value of $$1000,$ but $A$ is a zero$-$coupon bond, and its current price is $$900,$ and bond B pays annual coupons and is priced at par. What do you expect will happen to the market prices of A and $B$ if the risk$-$free yield curve moves up by $1$ basis point? Specifically, what are the price change of bond A and bond $B?$