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In this question, the basis is 0.450 ((100-4.5)-95.05), the unexpired basis is 0.09.
Therefore the lock in rate needs to be 5.36% (100-(95.05+0.09)+0.5). Then shouldn’t the net payment be $2251.2 (5.36%*84000*6/12).
The answer shows an effective rate of 5.57% and a net payment of $2339.82.
Please tell me where I have made a mistake. Thanks.
They are not dealing in futures, but are dealing in options.
If they were dealing in futures themselves then using the lock-in rate gives the net affect of paying whatever the actual interest rate turns out to be together with the gain or loss on the futures.
Here, because they are dealing in options, we need to know what the futures price will be on the date of the transaction (not the lock-in rate) and it will be 94.81 as shown in the answer. This is compared with the exercise price to determine whether or not the option is exercised (and in addition there is the premium payable for the option).