SQL: Create new groups of Date Ranges from a Set of Date Ranges

I am trying to find an appropriate title for my question and so far it's been 30 minutes of trying... :) So far I have the following example DateFrom DateTo Amount 2015/01/01 2015/08/31 1$ 2015/01/01 2015/12/31 3$ 2015/08/01 2015/12/31 7$ For the first line we get that we have 0.125$/month (1$/8 months) For the 2nd line we get that we have 0.25$/month (3$/12 months) For the 3d line we get that we have 1.4$/month (7$/5 months) Considering the above, we would like to create a new group of date ranges in order to have the sums of the amounts. Something like the results below: DateFrom DateTo Amount 2015/01/01 2015/07/31 (0.125$+0.25$)*7 =2.625$ 2015/08/01 2015/08/31 (1.4$+0.125$)*1 =1.775$ 2015/09/01 2015/12/31 (1.4$+0.25$)*4 =6.6$ The sum of the above is 11$ just like the original data. The result we want is actually the sum of the amount per unique group of date ranges. Is this possible to be achieved with SQL?