how do I forecast a 15% increase over 7 months?

Excel 2003

I have a YTD actual productivity number and need to forecast what the
productivity would need to be over each of the next 7 months to achieve a 15%
full year increase. The result would need to include the Headcount
reduction/increase for each month.

Productivity = (transaction/headcount)*(YTD Sales Days/monthly Sales Days)

I have each month's transactions, YTD Sales days and montly Sales Days.

Is this possible?

Do you mean to say have estimates of transactions, YTD sales days, and
monthly sales days already projected for the next 7 months? If so, and
if you're assuming those numbers are static, then yes, you should be
able to similarly project staffcount by figuring out the year-end
number and working backward.