Question

The employee time clock is accurate out to 3 decimal places and calculates the hours that an employee worked on their shift. The software calculating the weekly pay only uses ONE decimal position for hours. The hourly pay rate is $12.35. Would the employee lose or gain money if the hours were rounded? (Hint: Add all hours, THEN round the total based upon one significant decimal position for the time. Look at the value in the second decimal position to see if it is 5 or more. US currency has only two decimal places. Is any rounding done?) Monday 6.346 hours Tuesday 7.061 hours Wednesday 8.496 hours Thursday 7.739 hours Friday 6.491 hours Provide the following as part of your answer . 1. How many hours did the employee work? 2. How much did they make in the week? 3. If pay were calculated daily and then totaled, what (if any) difference would be in the paycheck? 4. Optional (extra points): If any hours worked, less than .125 were rounded down to zero and any hours worked above .725 were rounded up to 1 hour, how would that change the answers to questions 1-3 above?

Answer 1

1.Calculation of total no. of hours employee worked:-

Total no.of hours = 6.3 + 7.1 + 8.5 + 7.7 + 6.5 = 36.1 hours

Note:- Rounded off to 1 decimal point as the software uses one decimal point for hours.

2.Calculation of total earnings for no. of hours worked:-

Earnings per hour = $12.35

Earnings for 36.1 hours = $12.35 * 36.1 = $445.835 = $445.84 (rounded off to 2 decimal places as US currency has 2 decimals points)

3.Calculation of difference:-

calculation of daily earnings:

Monday = 6.3 * $12.35 = $77.805 = $77.81

Tuesday = 7.1 * $12.35 = $87.685 = $87.69

Wednesday = 8.5 * $12.35 = $104.975 = $104.98

Thursday = 7.7 * $12.35 = $95.095 = $95.10

Friday = 6.5 * $12.35 = $80.275 = $80.28

Total earnings = $77.81 + $87.69 + $104.98 + $95.10 + $80.28

= $445.86

Difference = $445.86 - $445.84 = $0.02

Therefore,If the hours were rounded and pay is calculated weekly the employee would lose. If the pay is calculated daily then the employee would gain.

4.Calculation of earnings if hours worked less than .125 were rounded to zero and if hours worked more than .725 rounded up to 1 hour:-

a. Calculation of total no. of hours employee worked = 6.3 + 7 + 8.5 + 8 + 6.5 = 36.3 hours

b. Calculation of total earnings for no. of hours worked = 36.3 * $12.35 = $448.305 = $448.31

c. calculation of daily earnings:

Monday = 6.3 * $12.35 = $77.805 = $77.81

Tuesday = 7 * $12.35 = $86.45

Wednesday = 8.5 * $12.35 = $104.975 = $104.98

Thursday = 8 * $12.35 = $98.8

Friday = 6.5 * $12.35 = $80.275 = $80.28

Total earnings = $77.81 + $86.45 + $104.98 + $98.8 + $80.28

= $448.32

Difference = $448.32 - $448.31 = $0.01