Spreading budget over months

I need to have a Project Management formula where the budget total is input, and different stage dates are put in and the budget will spread between the dates across the year. The yellow fields are those that could change by the project. The percentages are the amount of the total budget allocated to that work. Here is a shot of what I made structurally:

sheet1.png

The first row should show the budget spread between January and March for Design work, while the remaining budget should spread between the construction months.

Thanks for the help all

Thanks ma'am, attached is the worksheet

budget spread formulas.xlsx

No one has an idea how I can do this? I keep trying different methods but I can't get it to spit out the numbers over time with variable dates.

The actual dollars should be divided out between the real dates, but the spend should show at the month level. For the $1,000,000 example the money would divide out for two full and one half month:
January: $400,000 (40%)
February: $400,000 (40%)
March: $200,000 (20%)

I've tried dividing it out to the day then multiplying by days per month but of course the number of days vary. When I have gotten a close approximation of what I need it would start the financial spread at January 1 instead of the actual starting date.

Anyone have any kind of solutions?