Excel or math question

[emilpull]

[TABLE="width: 500"]
<tbody>[TR]
[TD][/TD]
[TD]Total peons[/TD]
[TD]Per Peon income/h[/TD]
[TD]Peon loss/h[/TD]
[TD]Time calculated[/TD]
[TD]Totalgold[/TD]
[/TR]
[TR]
[TD]Player1[/TD]
[TD]10000[/TD]
[TD]2.5[/TD]
[TD]3%[/TD]
[TD]n[/TD]
[TD]???[/TD]
[/TR]
[TR]
[TD]Player2[/TD]
[TD]11000[/TD]
[TD]2.5[/TD]
[TD]3%[/TD]
[TD]n[/TD]
[TD]???[/TD]
[/TR]
[TR]
[TD]Player3[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
</tbody>[/TABLE]

So, this is probably more a math problem than an excel problem. But while trying to simulate a game, I've come up with this problem. I want to be able to manipulate a number of constants (listed above) to give me the total gold gained over whatever unit of time.

The answer for player one would be:

10000*2.5 = 25000 for hour 1
10000*0.97*2.5 + 25000 (from hour 1) = 49250 for hour 2
9700*0.97*2.5 + 49250 (from hour 2) = 72772,5 for hour 3
etc...

I can sheet this out for one player using large tables and per time unit calculations, but I'm sure there's a way to do these calcs logarithmically, but can't for the life of me remember enough of my high school math...

 

[fhqwgads]

hope this works

Book1
	A	B	C	D	E	F
1		Total peons	Per Peon income/h	Peon loss/h	Time calculated	Totalgold
2	Player1	10000	2.5	0.03	1	25000
3	Player1	10000	2.5	0.03	2	49250
4	Player1	10000	2.5	0.03	3	72772.5
5	Player1	10000	2.5	0.03	4	95589.3
6	Player1	10000	2.5	0.03	5	117722
7	Player2	11000	2.5	0.03	1	27500
Sheet14

Cell Formulas
Range	Formula
F2	=($B2*$C2)*(1+-$D2)^(E2-1)+(($B2*$C2)*(1+-$D2)^(E2-1)-($B2*$C2))/-$D2

 

[phmalu]

[TABLE="width: 500"]
<tbody>[TR]
[TD][/TD]
[TD]Total peons[/TD]
[TD]Per Peon income/h[/TD]
[TD]Peon loss/h[/TD]
[TD]Time calculated[/TD]
[TD]Totalgold[/TD]
[/TR]
[TR]
[TD]Player1[/TD]
[TD]10000[/TD]
[TD]2.5[/TD]
[TD]3%[/TD]
[TD]n[/TD]
[TD]???[/TD]
[/TR]
[TR]
[TD]Player2[/TD]
[TD]11000[/TD]
[TD]2.5[/TD]
[TD]3%[/TD]
[TD]n[/TD]
[TD]???[/TD]
[/TR]
[TR]
[TD]Player3[/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
[TR]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[TD][/TD]
[/TR]
</tbody>[/TABLE]

So, this is probably more a math problem than an excel problem. But while trying to simulate a game, I've come up with this problem. I want to be able to manipulate a number of constants (listed above) to give me the total gold gained over whatever unit of time.

The answer for player one would be:

10000*2.5 = 25000 for hour 1
10000*0.97*2.5 + 25000 (from hour 1) = 49250 for hour 2
9700*0.97*2.5 + 49250 (from hour 2) = 72772,5 for hour 3
etc...

I can sheet this out for one player using large tables and per time unit calculations, but I'm sure there's a way to do these calcs logarithmically, but can't for the life of me remember enough of my high school math...

It is somewhat simple. First you must calculate the exponential decay equation that gives the amount of gold generated per hour (e. G 25,000 first, 24,250 second...) then you can simply integrate and that should give you the total amount over the desired period of time.
If nobody else does that for you in the next few hours I can when I get the chance to.