Final answer:
Company A will pay more in year 10, specifically $6,100 more than Company B. The calculation for each company's year 10 salary demonstrates that Company A's annual raises result in a higher total salary by that time. The correct answer is: b. Company A pays more.
Step-by-step explanation:
To determine which company will pay more in year 10 and by how much, we can calculate the total salary each company offers by the tenth year including their respective annual raises.
For Company A, the initial salary is $26,000 and it offers a $1,600 raise each year. By year 10, the total salary paid can be found by the formula for the sum of an arithmetic sequence: total salary = initial salary + raise × (number of years - 1). This gives us $26,000 + $1,600 × (10 - 1)
= $26,000 + $1,600 × 9
= $26,000 + $14,400
= $40,400.
For Company B, the initial salary is $28,000 with an annual raise of $700. Using the same formula, the total salary by year 10 would be $28,000 + $700 × (10 - 1)
= $28,000 + $700 × 9
= $28,000 + $6,300
= $34,300.
Therefore, by the tenth year, Company A would pay more. The difference between Company A and Company B's salaries in year 10 is $40,400 - $34,300 = $6,100.
The correct answer is: b. Company A pays more.