Q1. Two Year rate zero is currently trading at 2.0% yield and FIVE year zero trading at 2.5% rate. Overnight cash yield is 1.5%

1a. What is the duration for cash, 2y and 5y bond respectively?

1b. You think yield curve will flatten as Fed raises short term federal fund rate. If you LONG 10 million of 5Y bond, how many dollars of short position do you need to take in the 2Y in order to offset the dollar duration risk?

Please show all work for all question including equations.