swaps - reading 35

question 4, reading 35, in the answer, where does 1.070024 come from? After we overpay the swap by $0.952, why do we have to multiply by 1.070024?

after you get the 0.952 overpayment, the question then asks what the cumulative overpayment is in year 2. so assuming you “overpaid” by $0.952, you have to “borrow” that amount. the rate you borrow at is the 1 year rate 1 year forward. to get that you solve for x in this equation: (1.06)(1+x)=(1.065)^2 x = 1.070024