To compare the two options, we need to calculate the total earnings for each option over the 4-year period.
Option 1: Earning an additional $500 each year
The total earnings for this option will be:
Year 1: $15,000
Year 2: $15,500 ($15,000 + $500)
Year 3: $16,000 ($15,500 + $500)
Year 4: $16,500 ($16,000 + $500)
Total earnings over 4 years = $15,000 + $15,500 + $16,000 + $16,500 = $63,000
Option 2: Earning 2% of current salary
To calculate the earnings for this option, we need to find the salary for each year using the formula:
salary = $15,000 + 2% × (previous year's salary)
Year 1: salary = $15,000
Year 2: salary = $15,300 ($15,000 + 2% × $15,000)
Year 3: salary = $15,606 ($15,300 + 2% × $15,300)
Year 4: salary = $15,924.12 ($15,606 + 2% × $15,606)
Total earnings over 4 years = $15,000 + $15,300 + $15,606 + $15,924.12 = $61,830.12
Therefore, the first option of earning an additional $500 each year results in higher total earnings of $63,000 over 4 years, compared to earning 2% of the current salary, which results in total earnings of $61,830.12. Hence, the first option of earning an additional $500 each year is the better choice.