User:Est. 2021/sandbox/CURRENT

Formula

$X_{B}=1-{\frac {\operatorname {arsinh} \left({\sqrt {{\frac {1}{4}}+{\sqrt {1+\left({\frac {B}{S}}\right)^{2}}}-1}}-{\frac {1}{2}}\right)}{{\sqrt {{\frac {1}{4}}+{\sqrt {1+\left({\frac {B}{S}}\right)^{2}}}-1}}-{\frac {1}{2}}}}$

Legend & Data

$\operatorname {arsinh} =\sinh ^{-1}$
$S=3068$
$R$ = Total income
$N1$ = No-tax area
$B$ = Taxable income = if $R>N1$ , then $B=R-N1$ , otherwise $0$
$T$ = Tax = if $B>0$ , then $T=B*X_{B}=R*X_{R}$ , otherwise $0$

Tax Limit

$N0$ = Tax limit (%) $=Z_{R}$
$X_{R}=X_{B}*{\frac {B}{R}}$
$TZ$ = Limited tax = if $B>0$ , then $TZ=B*XZ_{B}=R*XZ_{R}$ , otherwise $0$

Tax Limit – Method 1

$XZ_{R}=X_{R}*Z_{R}=XZ_{B}*{\frac {B}{R}}=TZ:R$
$XZ_{B}=X_{B}*Z_{R}=XZ_{R}:{\frac {B}{R}}=TZ:B$
$Z_{B}={\frac {XZ_{B}}{X_{B}}}$

Tax Limit – Method 2

$XZ_{R}=$ if $X_{R}<Z_{R}$ , then $X_{R}$ , otherwise $Z_{R}$
$XZ_{B}=XZ_{R}:{\frac {B}{R}}$
$Z_{B}={\frac {XZ_{B}}{X_{B}}}=Z_{R}$