Impact of Rising Interest Rates on Fixed-Rate Payer in a Swap

Consider a fixed-for-floating interest rate swap where Company A agrees to pay a fixed interest rate of 3% on a notional amount of $1,000,000 to Company B, while Company B agrees to pay a floating interest rate tied to the 6-month LIBOR rate. The swap has a duration of 5 years.

At the initiation of the swap, if the market expects the LIBOR rates to rise above the fixed rate, which of the following statements is true regarding the value of the fixed-rate payer's position at a future date after the interest rates have risen?