Formula to split a value

Hello experts,

I’m looking for a Excel formula which enable to position the billing of a contract based on the Start and End dates of the contract (in my example, it is over 2 years 2014/01/01 to 2015/12/31), on to maturity (in my example, invoiced per quarter) and on the payment term (in my example = matured, i.e. I invoice at the beginning of quarter).
So I have to divide the annual value into 4 quarter (beginning of January; early April, early July, early October). Attached an example.
Thank in advance for help!
Regards