Consider a 2-year fixed for floating swap with a notional principal of $ 100. Payments are to be exchanged at the end of year 1 and year 2.  The floating rate at the beginning of each year defines the amount of floating payment.  For example, the floating rate at time 0 is 5% for year 1; this means $ 5 will be paid by the floating payer at the end of year 1 for each $ 100 of notional principal.  At time 0, the rates are as follows: a) 1 year rate is 5% per year, b) 2 year rate is 10% per year. 

The swap is fairly valued and no money changes hands at time zero. Find the dollar amount fixed payments per year in this scenario?