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Can someone help me with the formula needed to obtain the following. I need to discount products on a sliding scale. If a customer purchases 2 products, he must get a 15% discount. If he purchases 10, he must get a 30% discount. I don't want a linear slope, but rather as the number of products increases, the increase in the discount decreases.

2 => 15%
4 => ≈20%
10 => 30%

I need to formula with this, which should include a bend factor.

I know how do to this for FV, IV, but not this.

1 Answers 1

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You might want your discount function something like $$d(n) = 100 k_1 \times (1 - e^{-k_2 n})$$ where $d(n)$ is the percentage discount and $n$ is the number of products purchased and $k_1, k_2$ are constants with $0 < k_1 \leq 1$.

EDIT: Choose $k_1 = 0.31$ and $k_2 = 0.35$.

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    @Sirvam all the formulas you types are showing [Math Processing Error]2011-01-19
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    @IanC: Sorry I was editing it and then deleted it by mistake.2011-01-19
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    @Sirvam I'm still seeing errors for all the math.2011-01-19
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    Ok, works now... let me check it. :)2011-01-19
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    @Sirvam thanks, I can work with that. Is there an easy way to work out the values for k_1 and k_2 to get the 15% and 30% I desire?2011-01-19
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    @IanC: Choose $k_1 = 0.31$ and $k_2 = 0.35$ to get approximate discount values. $100 k_1$ gives the upper bound on the discount, $k_2$ gives the rate with respect to the number of objects at which you want increase/decrease the discount.2011-01-19
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    While this is in many ways the most mathematically elegant solution, good luck trying to explain it to your customers, @IanC.2011-01-19
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    @Rahul fortunately, they will never see it ;)2011-01-19