CFAI Volume 5 Risk Management-Plain Vanilla interest rate swap

Sample question in page 49 of Volume 5 Consider a plain vanilla interest rate swap with two months to go before the next payment. Six months after that, the swap will have its final payment. The swap fixed rate is 7%, and hte upcoming floating payment is 6.9%. All payments are based on 30 days in a month and 360 days in a year. Two-month LIBOR is 7.25%, and eight-month LIBOR 7.375%. The present value factors for two and eight months can be calculated as follow: 1/(1+0.0725*60/360) = 0.9881 1/(1+0.7375*240/360) =0.9531 The next floating payment will be 0.069*180/360 =0.0345. THe present value of the floating payments (Plus hypothetical notional principal) is 1.0345*0.9881 =1.0222. Given an annual reate of 7%, the fixed payments will be 0.07 *180/360 = 0.035 The present value of the fixed payments (plus hypothetical notional principal) is, therefore, 0.035*0.9881 + 1.035*0.9531 = 1.021 I am confused by the notional value of fixed payment and floating payment. Why do we need 1? To interest rate swap, the interest income is swapped, not principal . Thanks!

You don’t but they worked out the PV of the fixed side not the fixed interest payments.