If I’m not wrong we can calculate futures rate in 2 ways( using normal predicted futures rate & unexpired basis predicted futures rate 1.8986 + [(1.9156-1.8986)x2/7] = 1.903 ( same as the answer ) Or 1.9045 + [ 1/3 x (1.9045-1.8986) ] = 1.906 ( I’m not sure why this is not same as the answer…)
The second way is OK, except that you should be subtracting (1/3 x (1.9045 – 1.8986)) and not adding.
Think about it, since here the December futures price is lower than September futures price, then the 5 month futures price must be between the two and therefore less than the September futures price!!!