CFA Curriculum Vol 4 Page 396 Question 4: Suppose that oil forward price for 1 yr, 2 yr and 3 yr are $20, $21, $22. The 1-yr effective annual interest rate is 6%, 2-yr interest rate is 6.5%, and the 3-yr interest rate is 7%. Suppose you are the fixed-rate payer in the swap. Verify that the cumulative over-payment is zero after the third swap payment. Fair swap rate is $20.952. 1st year overpayment is $0.952 ($20.952-$20). In year 2, this overpayment has increased to $0.952x1.070024. And year 3, overpayment is $0.97066x1.08007. My question: How to determine the multiple for overpayment, e.g. 1.070024 for year 1 and 1.08007 for year 2. Thanks!

implied forward rates

1.065^2 / 1.06^1 = 1.070024 1.07^3 / 1.065^2 = 1.080071

Thanks so much!