Staff reduction rate from annualized to monthly rates

[drawingblankz]

Hi,

If I have 100 staff at the beginning of the financial year and is ordered to reduce the workforce by 12%, ie I should have 88 on average at the end of the year. How would I calculate the monthly percentage so the reduction of staff can be rolled out gradually. I don't want to cut 12 in the first month then do nothing for the rest of the year but that's not logical for the remaining staff.

If I cut 1 each month ie staff level in the first month is 99, 2nd month 98 etc, 12th month 88. but the average staff is not 88 ie (99+98+97+...88)/12 is 93.50.

If you could help it would be great. thanks.

Steph

 

[I like Serena]

Hi,

If I have 100 staff at the beginning of the financial year and is ordered to reduce the workforce by 12%, ie I should have 88 on average at the end of the year. How would I calculate the monthly percentage so the reduction of staff can be rolled out gradually. I don't want to cut 12 in the first month then do nothing for the rest of the year but that's not logical for the remaining staff.

If I cut 1 each month ie staff level in the first month is 99, 2nd month 98 etc, 12th month 88. but the average staff is not 88 ie (99+98+97+...88)/12 is 93.50.

If you could help it would be great. thanks.

Steph

Hi drawingblankz, welcome to MHB!

The problem asks for a monthly percentage.
It's not asking for an average staff of 88 over the year.
Instead it asks for a monthly percentage, so that at the end of the year we will have a staff of 88.

Let's give the monthly percentage a name and call it $r$.
Then after one month we have a workforce of $100(1-r)$.
That means that if we would pick $r=1\%=0.01$, that we would have $100(1-0.01)=99$ - same as in your example.

After 2 months that will be $100(1-r)^2$.
And so on, so that after 12 months we have a workforce of $100(1-r)^{12}$, which is supposed to be 88.
Can you find $r$ from that?