Question

What is the annual and semimonthly salary if the weekly salary is $820? show work

Answer 1

We are given a weekly salary of a person as follows:

`\text{Salary ( week ) = }\frac{\text{\$280}}{\text{week}}`

We have expressed the payroll of a worker as a " Rate " that means that salary is always on time basis. Hence, the amount of salary received by any worker is time dependent.

Any change in the time frame will also change the amount of salary accordingly. We will how this change is perceived.

We will first write down the number of weeks that occur in a year ( anually ) as follows:

`\textcolor{#FF7968}{1}\text{\textcolor{#FF7968}{ year = 52 weeks}}`

To determine the annual salary of the worker we will work with the units of the salary given per week as follows:

`\text{Salary ( annual ) = Salary ( week ) }\cdot\text{ }\frac{52\text{ weeks}}{year}`

We will plug in the respective quanitities in the above expression as follows:

`\begin{gathered} \text{Salary ( annual ) = }\frac{\text{\$820}}{week}\cdot\frac{52\text{ weeks}}{year} \\ \\ \text{\textcolor{#FF7968}{Salary ( annual ) = }}\textcolor{#FF7968}{\frac{\text{\$}42,640}{\text{year}}} \end{gathered}`

In the similar fashion we will write down the number of weeks in half of a month as follows:

`\text{\textcolor{#FF7968}{semi}}\textcolor{#FF7968}{-}\text{\textcolor{#FF7968}{month = }}\textcolor{#FF7968}{2.17262}\text{\textcolor{#FF7968}{ weeks}}`

To determine the semi-monthly salary of the worker we will work with the units of the salary given per week as follows:

`\text{Salary ( semi-monthly ) = Salary ( week ) }\cdot\text{ }\frac{2.17262\text{ weeks}}{\text{semi}-\text{month}}`

We will plug in the respective quanitities in the above expression as follows:

`\begin{gathered} \text{Salary ( semi-monthly ) = }\frac{\text{\$820}}{week}\cdot\frac{2.17262\text{ weeks}}{\text{semi}-\text{month}} \\ \\ \text{\textcolor{#FF7968}{Salary ( semi-monthly ) = }}\textcolor{#FF7968}{\frac{\text{\$}42,640}{\text{semi-month}}} \end{gathered}`

The answers can be summarized as follows:

`\begin{gathered} \text{\textcolor{#FF7968}{Salary ( annual ) = }}\textcolor{#FF7968}{\frac{\text{\$}42,640}{\text{year}}} \\ \\ \text{\textcolor{#FF7968}{Salary ( semi-monthly ) = }}\textcolor{#FF7968}{\frac{\text{\$}42,640}{\text{semi-month}}} \end{gathered}`