You are given an incomplete specification of the term structure, as specified by the spot rates and forward rates noted next. You also know that the price of a 6-year bond with coupon rate $10 %$ is $\$ 145.749$ and the price of a 6 -year bond with coupon rate $5 %$ is $\$ 100.315$. For all bonds, the face value is $\$ 100$, and the coupons are paid annually. Assuming continuous compounding, find the missing rates.

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$1=?, $26.9%, 83 = 7.5%, 84 =?, $5 = 8.4%, $6 =? f1.2 7.8%, f2,3=8.7%, fs,6 =?, f1,3 = 8.25%, f2.4 = 11.55%