I found this tricky as well to be honest, although it seemed easy. I went for 100... A floating rate note (which can be considered as the floating leg of the swap) would be valued at 100 on reset day or at initiation of the contract. Since it mentioned that the swap was valued at par, I thought I am in one of these situations. I was able to replicate the 100.95 answer but can't remember how.I felt something was missing from the IRS question. The 2 year swap payed 6% fix and vas valued at par. I.e. Was worth zero. The question was the value of the floating leg with ois rates 5% for first year and 5.5% for 2 years. I think you need the current libor fixing and the forward rate from first to second year to solve this. From the information, that the swap is valued at par you can get one unknown, but you are still missing the second. Or am I missing something here.
I solved it by assuming that the current fixing and the forward rate are both 6%. Dont know if result is correct, i think other solutions are possible.