Final answer:
To find the employee's salary at the end of the 9th year, use the arithmetic sequence formula An = A1 + (n - 1) × d. The salary at the end of the 9th year is calculated to be $55,200.
Step-by-step explanation:
To determine the annual salary at the end of the 9th year for an employee whose starting salary is $36,000 with an increase of $2,400 each year, we can use an arithmetic sequence formula. The salary structure forms an arithmetic sequence where each year the salary increases by a fixed amount.
The formula to find the nth term of an arithmetic sequence is given by:
An = A1 + (n - 1) × d
where:
- An is the nth term (the salary at the end of the 9th year in this case)
- A1 is the first term (the starting salary)
- n is the term number (9 for the 9th year)
- d is the common difference (the annual increase)
Applying the values from the question:
A9 = $36,000 + (9 - 1) × $2,400
A9 = $36,000 + (8) × $2,400
A9 = $36,000 + $19,200
A9 = $55,200
So, the annual salary at the end of the 9th year is $55,200.