Find required increase per day. Find X

Question

So I need help with formula.

We have a price that is published every day for example today's was $23995.

We also have a month to date, which is obviously the average of all the daily prices this month which is 21308.

We predict that the the average price for the month will be $23750. To achieve this the price will need to average 27718.25 for the remaining 8 days of the month.

Or an increase of x per day.

We need a formula to find x. Its roughly $1000, but how can i work this out exactly? the problem I have is each day we add 1000 the month to date will change...

Thanks for reading all this. I'm sure I could have explained it better?? Thanks for your help!

Answer 1

Based off the numbers you have provided, the $21308$ month-to-date average already includes today's price. If this changes, the setup I'm giving below can be changed slightly to work.

Define the following variables:

• $avg_{cur} = $ the current month-to-date average ($21308$ for original example)
• $avg_{month} = $ the predicted average price for the month ($23750$ for original example)
• $days_{total} = $ the total number of working days in the month ($21$ for original example)
• $days_{down} = $ the number of working days done this month, including current day ($13$ for original example)
• $days_{left} = days_{total}-days_{down}$, the number of days left in the month ($8$ for original example)
• $price = $ the price today ($23995$ for original example)
• $X = $ the increase in price needed per day

Start like you would for finding the daily average needed and calculate $avg_{month}*days_{total}-avg_{cur}*days_{down}$. (This comes out to $221746$ for the original example and divided by $days_{left} = 8$ gives the daily average of $27718.25$.) What we want to find is a per day price increase $X$ such that $$(price+X)+(price+2X)+...+(price+(days_{left})X) = avg_{month}*days_{total}-avg_{cur}*days_{down}.$$

A little algebra on the left hand side turns the equation into $$days_{left}*price+\dfrac{days_{left}(days_{left}+1)}{2}*X = avg_{month}*days_{total}-avg_{cur}*days_{down}.$$

Solving for $X$ yields $$X = \dfrac{2}{days_{left}(days_{left}+1)}(avg_{month}*days_{total}-avg_{cur}*days_{down}-days_{left}*price)$$

So for the original example, we get $$X = \dfrac{2}{8*9}(23750*21-21308*13-23995*8) \approx 827.39$$