Question

Develop an algorithm to compute gross pay. The inputs to your algorithm are the hours worked per week and the hourly pay rate. The rule for determining gross pay is to pay the regular pay rate for all hours worked up to 40 , time-and-a-half for all hours over 40 up to 54 , and double time for all hours over 54 . Compute and display the value for gross pay using this rule. After displaying one value, ask the user whether he or she wants to do another computation. Repeat the entire set of operations until the user says no.

Short answer

Calculate pay for regular, overtime, and double time hours, then sum them for total gross pay. Repeat if requested by user.

Step-by-step solution

Gather Inputs

Begin by asking the user to input the number of hours worked per week and the hourly pay rate. Ensure both inputs are correctly stored in variables, for example, `hours_worked` and `hourly_rate`.

Determine Regular Hours

Check if the `hours_worked` is less than or equal to 40. If it is, then all the hours are considered regular hours.

Calculate Regular Pay

Calculate regular pay by multiplying regular hours by the `hourly_rate`. Use the formula: \[\text{Regular Pay} = \min(40, \text{hours extunderscore worked}) \times \text{hourly extunderscore rate}\]

Determine Overtime Hours Up to 54

If `hours_worked` is greater than 40 but less than or equal to 54, calculate the additional hours for which overtime pay is applicable at time-and-a-half. Use the formula: \[\text{Overtime extunderscore hours} = \max(0, \min(54, \text{hours extunderscore worked}) - 40)\]

Calculate Overtime Pay

Calculate the overtime pay at time-and-a-half using the formula: \[\text{Overtime Pay} = \text{Overtime extunderscore hours} \times \text{hourly extunderscore rate} \times 1.5\]

Determine Double Time Hours

If `hours_worked` exceeds 54, calculate the number of hours for which double time applies: \[\text{Double extunderscore time extunderscore hours} = \max(0, \text{hours extunderscore worked} - 54)\]

Calculate Double Time Pay

Calculate double time pay using the formula: \[\text{Double extunderscore Time Pay} = \text{Double extunderscore time extunderscore hours} \times \text{hourly extunderscore rate} \times 2\]

Compute Total Gross Pay

Sum the regular pay, overtime pay, and double time pay to find the total gross pay: \[\text{Gross extunderscore Pay} = \text{Regular Pay} + \text{Overtime Pay} + \text{Double extunderscore Time Pay}\]

Display Results

Output the total gross pay calculated to the user.

Offer to Repeat Calculation

Ask the user if they would like to compute the gross pay for another set of inputs. Repeat the process if the user answers affirmatively; otherwise, end the program.

Key concepts

Gross Pay Calculation

When calculating gross pay, you need to understand how different types of hours are paid. Gross pay refers to the total earnings before any deductions, like taxes, are taken. The calculation starts by determining regular hours worked, which is up to 40 hours per week. For these hours, employees earn their standard hourly rate. Let's assume the standard hourly rate is given as part of the input. If an employee works 40 hours exactly, gross pay is simply:
\[\text{Gross Pay} = \text{hours extunderscore worked} \times \text{hourly extunderscore rate}\]
For example, if an employee works 38 hours and has an hourly rate of \(20, the gross pay calculation would be 38 hours times \)20, equaling $760. But calculating gross pay gets a little more complex when overtime and double time hours come into play.

Overtime Calculation

Overtime calculation becomes important when an employee works more than 40 hours but not more than 54 hours in a given week. The hours that fall between this range are considered overtime hours, and they are compensated at time-and-a-half. This means the pay rate for these hours is 1.5 times the regular hourly rate. To find overtime pay, determine how many hours exceed the regular 40-hour threshold up to 54 hours, and then apply the overtime multiplier:
\[\text{Overtime extunderscore Pay} = (\text{hours extunderscore worked} - 40) \times \text{hourly extunderscore rate} \times 1.5\]
If an employee works 50 hours at a \(20 rate per hour, they will have 10 overtime hours. Their overtime pay would be 10 times \)20, and then this result multiplied by 1.5, totaling $300.

Double Time Calculation

Double time calculation is relevant for employees who work more than 54 hours in a week. For each hour worked beyond the 54-hour mark, they earn double their standard time pay. This compensation scheme ensures that long hours are remunerated at a higher rate, providing additional incentives for employees. To calculate the double time pay, find the number of hours above 54, and double the standard hourly rate for these hours:
\[\text{Double extunderscore Time Pay} = (\text{hours extunderscore worked} - 54) \times \text{hourly extunderscore rate} \times 2\]
Consider an employee who works 60 hours at \(20 per hour. They work 6 hours beyond 54 hours, earning \)240 in double time pay. Adding this to their regular and overtime pay results in their total gross pay for the week.