Hatrack River Forum: Math question (mayfly)

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Posted by Lisa (Member # 8384) on :

I don't know. Maybe if I wasn't sick, I'd be able to figure this out myself. Maybe not.

I have a spreadsheet with budget numbers to be input programmatically. And I need to let the user input a number, and have it spread across 12 months, such that each month is X% higher than the previous month.

I can't figure out how to calculate it. As far as I can see, it's a series. If A is the total that's getting spread, and B is what gets multiplied on each month (1 + X%) and C is the amount that gets put in the first month, I have something like this:

A = C + CB + CB^2 + Cy^B + ... +CB^11

And I have A and B, so it should be possible to solve for C. But I can't do it. O Brains of Hatrack, can you help me?

Posted by Dagonee (Member # 5818) on :

Divide by C:

A/C = 1 + B + B^2...

Divide by A:

1/C = (1 + B + B^2...)/A

Take the reciprocal (the only step I'm questionable about - seems if we know C and A are non-zero, should be ok):

C = A/(1 + B + B^2...)

Posted by Stephan (Member # 7549) on :

Would it look like this as a very simple example?

http://i22.photobucket.com/albums/b315/ocnomad/test.gif

Posted by Stephan (Member # 7549) on :

5% higher in my example

Posted by Icarus (Member # 3162) on :

quote:
Originally posted by Dagonee:
Divide by C:

A/C = 1 + B + B^2...

Divide by A:

1/C = (1 + B + B^2...)/A

Take the reciprocal (the only step I'm questionable about - seems if we know C and A are non-zero, should be ok):

C = A/(1 + B + B^2...)

Or you could factor out C and divide by (1 + B + B^2...) on both sides. That quantity can't be zero unless X = -100%, which I doubt.

Posted by Dagonee (Member # 5818) on :

Right. I knew that. *whistles innocently*

Posted by Lisa (Member # 8384) on :

quote:
Originally posted by Dagonee:
Divide by C:

A/C = 1 + B + B^2...

Divide by A:

1/C = (1 + B + B^2...)/A

Take the reciprocal (the only step I'm questionable about - seems if we know C and A are non-zero, should be ok):

C = A/(1 + B + B^2...)

Okay, now, that's just embarrassing.

Thanks, Dagonee. I should have seen that.

Posted by Bokonon (Member # 480) on :

Icarus did it the way I would have. And even if X = -100%, you are left with C = A, which is trivial to watch out for [Smile]

Factoring is fun!

-Bok