How do I calculate a cumulative reducing percentage for forecasting?

[gazzap]

I have a maths problem that has confused me.
Each month I have a performance score. Month by month those scores are added together to make a cumulative score of the year to date.
There is a target (percentage) that must be achieved by the year end. Based on the current cumulative result I need to find what the result has to be in all of the remaining months in order to hit the target exactly.

For example
Month 1 result: 93 out of 100 (93%)
Month 2 result: 71 out of 100 (cumulative result is now 82%, 164 out of 200)

Target for year is 75%.

So, in the remaining 10 months, the result each month would have to be less than 75% (because it is currently 7% above the target). But what is the formula to calculate that figure?
Each month going forward, the real result will be entered, and of course this will have an effect on this figure.
I know the answer to the example is 73.9%, achieved purely using trial and error but I cannot create the formula to find the answer.
Using this figure I can see that the cumulative result changes more in the first month than the second and the second is more than the third and so on. ie the change is in ever decreasing amounts until the target is hit.
I don't know what the name of this maths problem is.
Can anyone help?

 

[HallsofIvy]

I have a maths problem that has confused me.
Each month I have a performance score. Month by month those scores are added together to make a cumulative score of the year to date.
There is a target (percentage) that must be achieved by the year end. Based on the current cumulative result I need to find what the result has to be in all of the remaining months in order to hit the target exactly.

For example
Month 1 result: 93 out of 100 (93%)
Month 2 result: 71 out of 100 (cumulative result is now 82%, 164 out of 200)

Target for year is 75%.

So, in the remaining 10 months, the result each month would have to be less than 75% (because it is currently 7% above the target). But what is the formula to calculate that figure?

You need to use "raw" numbers rather than percentages but if that "out of 100" stays constant, then you can just treat the percentages as if they were "raw" numbers. If you want 75% 0ver the 12 months of the year, then you want a raw score if 0.75*1200= 900. You already have 93+ 71= 164, as you say. So you want a total of 900- 164= 736 over the next 10 months. That is an average of 73.6 for each month so you will want 73.6%, not 73.9%, of 100 each month.

Each month going forward, the real result will be entered, and of course this will have an effect on this figure.
I know the answer to the example is 73.9%, achieved purely using trial and error but I cannot create the formula to find the answer.
Using this figure I can see that the cumulative result changes more in the first month than the second and the second is more than the third and so on. ie the change is in ever decreasing amounts until the target is hit.
I don't know what the name of this maths problem is.
Can anyone help?

 

[gazzap]

Unfortunately the number isn't always out of 100 each month. I was using that to simplify the example so that the number would equal the percentage in the example but in reality the numbers are basically random. If I knew the total for the year was going to be out of 1200 then yes it would be far easier.