The easiest way to see what is going on is probably to draw a diagram, which in this case is a triangle. if the risk increases uniformly from 0 to 2 over the year then 7/8ths of the way through the year, the risk must be 2*7/8 per day. To work out what is earned you work out the area of the triangle for the piece that is earned and divide it by the total amount of risk (ie the area of the full annual triangle - which is 1=1/2*1*2). The area of the triangle for the piece that is earned is therefore 1/2 * 7/8 * 2*7/8 which is 49/64 (using the formula for the area of a triangle which is 1/2*base*height).