Subjects financial math

Pay Calculations 43C790

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1. **Problem 10a:** Jim receives holiday loading of 17.5% of 4 weeks pay, and the loading amount is 996.80. We need to find his normal weekly pay. 2. The formula for holiday loading is: $$\text{Holiday Loading} = 0.175 \times 4 \times \text{Weekly Pay}$$ 3. Substitute the known values: $$996.80 = 0.175 \times 4 \times \text{Weekly Pay}$$ 4. Simplify the right side: $$996.80 = 0.7 \times \text{Weekly Pay}$$ 5. To find Weekly Pay, divide both sides by 0.7: $$\text{Weekly Pay} = \frac{996.80}{0.7}$$ 6. Show cancellation: $$\text{Weekly Pay} = \frac{\cancel{996.80}}{\cancel{0.7}} = 1424$$ 7. So, Jim's normal weekly pay is $1424. 8. **Problem 10b:** Find Jim's normal hourly pay rate if he works 40 hours a week. 9. Hourly pay rate formula: $$\text{Hourly Pay} = \frac{\text{Weekly Pay}}{\text{Hours per week}}$$ 10. Substitute values: $$\text{Hourly Pay} = \frac{1424}{40}$$ 11. Simplify: $$\text{Hourly Pay} = 35.6$$ 12. Jim's normal hourly pay rate is $35.60. 13. **Problem 11a:** Chloe’s annual salary is 72800. Calculate her weekly wage. 14. There are 52 weeks in a year, so: $$\text{Weekly Wage} = \frac{72800}{52}$$ 15. Simplify: $$\text{Weekly Wage} = 1400$$ 16. Chloe’s weekly wage is $1400. 17. **Problem 11b:** Holiday loading is 17.5% of four weeks pay. Calculate Chloe’s holiday loading. 18. Calculate 4 weeks pay: $$4 \times 1400 = 5600$$ 19. Calculate holiday loading: $$0.175 \times 5600 = 980$$ 20. Chloe’s holiday loading is $980. 21. **Problem 11c:** Chloe’s employer increases her annual salary by 1%. Calculate new salary. 22. Increase amount: $$0.01 \times 72800 = 728$$ 23. New annual salary: $$72800 + 728 = 73528$$ 24. Chloe’s new annual salary is $73528. 25. **Problem 11d:** Explain why Chloe is worse off financially with the 1% increase. 26. Chloe loses holiday loading of $980 but gains only $728 from the 1% increase. 27. Since $728 < $980, she is worse off by $252. 28. So, the increase does not fully compensate for the lost holiday loading.