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mathmathematical-optimization

Summarize My Formula?

I would like to summarize my formula. p and y are constant value, 10000 and 0.65.

When n = 3, my formula recalculate the result of n = 2. I don't want to recalculate. Is there way to summarize or other formula for that equivalent?

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Update :

For More Info :

n=1 => 10000 * 0.65 = 6500
n=2 => (10000 + 6500) * 0.65 = 10725
n=3 => (10000 + 10725) * 0.65 = 13471.25

If I put n=3, I don't want to recalculate the result of n=1 and n=2.

Solution

  • To solve such problems you may use the z-Transformation. You actually need a value for x[0].

    The result for x[0]=0 is:

    x[k] = p*y * (1-y^k)/(1-y)

    From your posting it seems that you need exactly that.