Answer :
To determine which job offer will result in the least total earnings over seven years, we need to calculate the total cumulative salary for each job offer based on their starting salaries and annual percentage increases.
1. Calculations for the first offer (Starting salary: [tex]$125,000, increase rate: 2% per year): Yearly salaries would be: - Year 1: $[/tex]125,000
- Year 2: [tex]$125,000 (1 + 0.02) = $[/tex]127,500
- Year 3: [tex]$127,500 (1 + 0.02) = $[/tex]130,050
- Year 4: [tex]$130,050 (1 + 0.02) = $[/tex]132,651
- Year 5: [tex]$132,651 (1 + 0.02) = $[/tex]135,304
- Year 6: [tex]$135,304 (1 + 0.02) = $[/tex]138,011
- Year 7: [tex]$138,011 (1 + 0.02) = $[/tex]140,772
- Total salary over 7 years: [tex]$125,000 + $[/tex]127,500 + [tex]$130,050 + $[/tex]132,651 + [tex]$135,304 + $[/tex]138,011 + [tex]$140,772 = $[/tex]929,285.42
2. Calculations for the second offer (Starting salary: [tex]$110,000, increase rate: 3% per year): Yearly salaries would be: - Year 1: $[/tex]110,000
- Year 2: [tex]$110,000 (1 + 0.03) = $[/tex]113,300
- Year 3: [tex]$113,300 (1 + 0.03) = $[/tex]116,699
- Year 4: [tex]$116,699 (1 + 0.03) = $[/tex]120,200
- Year 5: [tex]$120,200 (1 + 0.03) = $[/tex]123,806
- Year 6: [tex]$123,806 (1 + 0.03) = $[/tex]127,520
- Year 7: [tex]$127,520 (1 + 0.03) = $[/tex]131,345
- Total salary over 7 years: [tex]$110,000 + $[/tex]113,300 + [tex]$116,699 + $[/tex]120,200 + [tex]$123,806 + $[/tex]127,520 + [tex]$131,345 = $[/tex]842,870.84
3. Calculations for the third offer (Starting salary: [tex]$98,000, increase rate: 8% per year): Yearly salaries would be: - Year 1: $[/tex]98,000
- Year 2: [tex]$98,000 (1 + 0.08) = $[/tex]105,840
- Year 3: [tex]$105,840 (1 + 0.08) = $[/tex]114,307
- Year 4: [tex]$114,307 (1 + 0.08) = $[/tex]123,451
- Year 5: [tex]$123,451 (1 + 0.08) = $[/tex]133,327
- Year 6: [tex]$133,327 (1 + 0.08) = $[/tex]144,893
- Year 7: [tex]$144,893 (1 + 0.08) = $[/tex]156,484
- Total salary over 7 years: [tex]$98,000 + $[/tex]105,840 + [tex]$114,307 + $[/tex]123,451 + [tex]$133,327 + $[/tex]144,893 + [tex]$156,484 = $[/tex]874,434.73
4. Calculations for the fourth offer (Starting salary: [tex]$105,000, increase rate: 4% per year): Yearly salaries would be: - Year 1: $[/tex]105,000
- Year 2: [tex]$105,000 (1 + 0.04) = $[/tex]109,200
- Year 3: [tex]$109,200 (1 + 0.04) = $[/tex]113,568
- Year 4: [tex]$113,568 (1 + 0.04) = $[/tex]118,111
- Year 5: [tex]$118,111 (1 + 0.04) = $[/tex]122,836
- Year 6: [tex]$122,836 (1 + 0.04) = $[/tex]127,749
- Year 7: [tex]$127,749 (1 + 0.04) = $[/tex]132,859
- Total salary over 7 years: [tex]$105,000 + $[/tex]109,200 + [tex]$113,568 + $[/tex]118,111 + [tex]$122,836 + $[/tex]127,749 + [tex]$132,859 = $[/tex]829,320.92
Now comparing the total salaries:
- Offer 1: [tex]$929,285.42 - Offer 2: $[/tex]842,870.84
- Offer 3: [tex]$874,434.73 - Offer 4: $[/tex]829,320.92
The least total earnings over seven years are from the fourth offer, which totals [tex]$829,320.92. Therefore, the worker will earn the least with: The fourth offer (Starting salary $[/tex]105,000 with a 4% increase each year).
1. Calculations for the first offer (Starting salary: [tex]$125,000, increase rate: 2% per year): Yearly salaries would be: - Year 1: $[/tex]125,000
- Year 2: [tex]$125,000 (1 + 0.02) = $[/tex]127,500
- Year 3: [tex]$127,500 (1 + 0.02) = $[/tex]130,050
- Year 4: [tex]$130,050 (1 + 0.02) = $[/tex]132,651
- Year 5: [tex]$132,651 (1 + 0.02) = $[/tex]135,304
- Year 6: [tex]$135,304 (1 + 0.02) = $[/tex]138,011
- Year 7: [tex]$138,011 (1 + 0.02) = $[/tex]140,772
- Total salary over 7 years: [tex]$125,000 + $[/tex]127,500 + [tex]$130,050 + $[/tex]132,651 + [tex]$135,304 + $[/tex]138,011 + [tex]$140,772 = $[/tex]929,285.42
2. Calculations for the second offer (Starting salary: [tex]$110,000, increase rate: 3% per year): Yearly salaries would be: - Year 1: $[/tex]110,000
- Year 2: [tex]$110,000 (1 + 0.03) = $[/tex]113,300
- Year 3: [tex]$113,300 (1 + 0.03) = $[/tex]116,699
- Year 4: [tex]$116,699 (1 + 0.03) = $[/tex]120,200
- Year 5: [tex]$120,200 (1 + 0.03) = $[/tex]123,806
- Year 6: [tex]$123,806 (1 + 0.03) = $[/tex]127,520
- Year 7: [tex]$127,520 (1 + 0.03) = $[/tex]131,345
- Total salary over 7 years: [tex]$110,000 + $[/tex]113,300 + [tex]$116,699 + $[/tex]120,200 + [tex]$123,806 + $[/tex]127,520 + [tex]$131,345 = $[/tex]842,870.84
3. Calculations for the third offer (Starting salary: [tex]$98,000, increase rate: 8% per year): Yearly salaries would be: - Year 1: $[/tex]98,000
- Year 2: [tex]$98,000 (1 + 0.08) = $[/tex]105,840
- Year 3: [tex]$105,840 (1 + 0.08) = $[/tex]114,307
- Year 4: [tex]$114,307 (1 + 0.08) = $[/tex]123,451
- Year 5: [tex]$123,451 (1 + 0.08) = $[/tex]133,327
- Year 6: [tex]$133,327 (1 + 0.08) = $[/tex]144,893
- Year 7: [tex]$144,893 (1 + 0.08) = $[/tex]156,484
- Total salary over 7 years: [tex]$98,000 + $[/tex]105,840 + [tex]$114,307 + $[/tex]123,451 + [tex]$133,327 + $[/tex]144,893 + [tex]$156,484 = $[/tex]874,434.73
4. Calculations for the fourth offer (Starting salary: [tex]$105,000, increase rate: 4% per year): Yearly salaries would be: - Year 1: $[/tex]105,000
- Year 2: [tex]$105,000 (1 + 0.04) = $[/tex]109,200
- Year 3: [tex]$109,200 (1 + 0.04) = $[/tex]113,568
- Year 4: [tex]$113,568 (1 + 0.04) = $[/tex]118,111
- Year 5: [tex]$118,111 (1 + 0.04) = $[/tex]122,836
- Year 6: [tex]$122,836 (1 + 0.04) = $[/tex]127,749
- Year 7: [tex]$127,749 (1 + 0.04) = $[/tex]132,859
- Total salary over 7 years: [tex]$105,000 + $[/tex]109,200 + [tex]$113,568 + $[/tex]118,111 + [tex]$122,836 + $[/tex]127,749 + [tex]$132,859 = $[/tex]829,320.92
Now comparing the total salaries:
- Offer 1: [tex]$929,285.42 - Offer 2: $[/tex]842,870.84
- Offer 3: [tex]$874,434.73 - Offer 4: $[/tex]829,320.92
The least total earnings over seven years are from the fourth offer, which totals [tex]$829,320.92. Therefore, the worker will earn the least with: The fourth offer (Starting salary $[/tex]105,000 with a 4% increase each year).
