- #1

gazzap

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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?