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The answer compares values by calculating the PV of both the fixed-rate side, and the index-return side.
In the index-return side, it takes the value of the index from the last swap payment (i.e. end of third quarter) and calculates its present value:
(Present Index / Index 30 Days Ago) * (Capital)
= (3150/3000)(5,000,000)
= $5,250,000
In the fixed-rate side, it takes the future value of the swap (at final payout, 60 days from now) and back-calculates its present value. You have to include the final payout when valuing the swap because it’s not paid out yet, hence the $50,000:
(60-Day Discount Factor)*(Capital + Final Payout)
= 0.9940 * ($5,000,000 + 1%*($5,000,000) )
= 0.9940 * ($5,050,000)
= $5,019,700
Why a 1% final payout? Because it’s a swap with 4% fixed rate at quarterly payouts, so you’ll get a payout each quarter at 1%.