User:FiveK/Taxable account after-tax balance

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Converting the summation into the closed form equation for the sum of a geometric series gives

Basis = P + P*d*(1-z)*((1+r-d*z)n - 1)/(r-d*z)

The amount available after withdrawal is EOY - w * (EOY - basis)

EOY = P*(1+r-d*z)^n

Basis = P + P*d*(1-z) * ((1+r-d*z)^n - 1)/(r-d*z)

Amount= (EOY-w*(EOY-Basis))

= P * ((1+r-d*z)^n*(r-d*z-(r-d)*w)+(r-d)*w)/(r-d*z)

Divide by P and let e = r-d*z

Amt/P	= (((1-(1+e)^n)*r+d*(1+e)^n-d)*w+e*(1+e)^n)/e

Let g = r-d

= ((g-(1+e)^n*g)*w+e*(1+e)^n)/e

Let f = w*g/e

= (1+e)^n*(1-f)+f

Amount after withdrawal = P * [(1+e)^n*(1-f)+f]