Question $5$

$[8]$

Suppose a natural person of $49$ years receives an annual salary of R$760000.$ The person has an investment yielding interest of R$2100$ per month and contributes R$4580$ per month to a pension fund. Assume that the following conditions are valid for a tax year for persons younger than $65$ years:

$\backslash$table$[[$Taxable Income,Tax rate,,,$],[0-237100,18\%$ of taxable income,,,$],[237101-370500,42678+26\%$ of amount above $237100,,,],[370501-512800,77362+31\%$ of amount above $370500,,,],[512801-673000,121475+36\%$ of amount above $512800,,,],[673001-857900,179147+39\%$ of amount above $673000,,,],[857901-1817000,251258+41\%$ of amount above $857900,,,],[1817001$ and above,$644489+45\%$ of amount above $1817000,,,],[$Interest exemption on investments,$],[$Maximum amount deductible from taxable income,$],[$Tax rebates,R$23800],[$Primary rebate on tax,R$17235],[$Contributions to annuities,R$350000]]$

$5\mathrm{.}1$ Determine the taxable income $x.$

$(4)$

$5\mathrm{.}2$ Use the information in the table and write the income taxT as a function of taxable income $x($piecewise function $T(x)),$ for this specific individual.

$(1)$

$5\mathrm{.}3$ Determine the tax $T(x),$ due by the person.