the Floating-Rate Payments As explained earlier, we must be careful about how we compute the present value of payments. In particular, we must carefully specify (1) the timing of the payment and (2) the interest rates that should be used to dis- count the payments. We have already addressed the first issue. In con- structing the exhibit for the payments, we indicated that the payments are at the end of the quarter. So, we denoted the time periods with respect to the end of the quarter. Now lets turn to the interest rates that should be used for discount- ing. First, every cash flow should be discounted at its own discount rate using a spot rate. So, if we discounted a cash flow of $1 using the spot rate for period t, the present value would be:   $1 presentvalueof$1tobereceivedinperiodt = ---------------------------------------------------------------------- (1+ spot rate for period t )t             Second, forward rates are derived from spot rates so that if we dis- counted a cash flow using forward rates rather than spot rates, we would come up with the same value. That is, the present value of $1 to be received in period t can be rewritten as:   present value of $1 to be received in period t = -------------------------------------------------------------------------------------------------------------------$----1-------------------------------------------------------------------------------------------------------------------- (1 + forward rate for period 1) ( 1+ forward rate for period 2) ¼(1 + forward rate for period t)     We will refer to the present value of $1 to be received in period t as the forward discount factor. In our calculations involving swaps, we will compute the forward discount factor for a period using the forward rates. These are the same forward rates that are used to compute the floating- rate payments-those obtained from the Eurodollar CD futures contract. We must make just one more adjustment. We must adjust the forward rates used in the formula for the number of days in the period (i.e., the quarter in our illustrations) in the same way that we made this adjustment to obtain the payments. Specifically, the forward rate for a period, which we will refer to as the period forward rate, is computed using the follow- ing equation:     periodforwardrate=