Let Ti, i=1, ,n be a set of dates, on which payments of the floating leg of an interest rate swap occur. The payoff of the floating leg of the swap at time Ti is Fi + s where Fi is the reference rate of the floating leg and s is a constant spread. For simplicity, let' s assume that the floating and fixed payments happen on the same dates. Also, ri is the risk-free rate on the same tenor. Let N be the notional of the swap.

1) What is the fixed semi-annual swap rate calculated from the risk-free rates? Please specify mathematical formula.

2) Let the semi-annual swap rate calculated in1) be the fixed leg payment of the swap. What is the constant spread which sets the present value of the swap position to be zero? Please specify mathematical formula.