Q$1.$ TWO Year rate zero is currently trading at $4\mathrm{.}80\%$ yield and ten year zero trading at $4\mathrm{.}40\%$ rate. Overnight cash yield is $5\mathrm{.}5\%$

Q$1$a$.$ What is the duration for cash, $2y$ and $10y$ bond respectively $(4$ points$)?$

Q$1$b$.$ You think yield curve will steepen as economy slows down and Fed cuts short term federal fund rate, AND also due to the massive coupon bond supply from Treasuries. If you LONG $100$ million of $2$ Y bond, how many dollars of short position do you need to take in the $10Y$ in order to offset the dollar duration risk? $(4$ points$)$