Calculating the future futures price!

Because we do not know either the spot rate or the futures price at the date of the transaction, we have to use the 'lock-in rate'. You can get it in two ways (and the examiners answer shows both ways). One way is the way I show in my lectures (taking the current spot rate and adjusting by the expired basis, or taking the current futures price and adjusting by the unexpired basis). The other way (provided that more than 1 current futures price is given, is to apportion between them. Here we need an effective futures price for the end of May, so apportion between the prices for March and for June futures.

It doesn't matter - there are arguments for both and either will do in the exam :-)