Mar/ jun 2016 future contracts

The first paragraph of the question states that 'now' is 1 March. Later in the question, it says that the receipt is in 3 months time, and that means the receipt will be at the end of May. For the futures the answer is calculating the lock-in rate. What the examiner has done is apportioned between the March and June futures prices in order to get a rate for the end of May. Alternatively, (as the examiner has written), the lock-in rate can be calculated using either the current spot or forward rates and adjusting by the change in the basis. The answer will be the same.

The March futures price is 0.8638, and the June futures price is 0.8656. There is 3 months between March and June, and the price changes by the difference of 0.0018 over the 3 months. We want the lock-in rate as at the end of May, which is 2 months after the end of March. Therefore the lock-in rate for May is 0.8638 + (2/3 x 0.0018) = 0.8650.