The key to calculating forward rates is to understand that the longer spot rate has to be equivalent to the product of the two shorter rates. In this case, an investment in a 1-year rate held over the year has to generate the same cash flow as investing for the first six months and then reinvesting in another 6-month bond. Therefore, the forward rate implied by the annual and the 6-month spot rate is equal to:
= 4.6831%
4.6831 x 2 = 9.37% annualized return
