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Question: Marquis begins a job making $53,000 per year. Each year, he is to receive a $1,600 raise. His…
Marquis begins a job making $53,000 per year. Each year, he is to receive a $1,600 raise. His salary after years can be modeled by this equation: . After 25 years, how much total money will Marquis have earned from this job?
$1,805,000
$1,845,000
$1,792,000
$1,844,975
Solution
Marquis’s salary after years is given by the equation: To find out how much total money Marquis will have earned after 25 years, we need to calculate the sum of his salary from year 1 to year 25. First, calculate the salary for year 1: Next, calculate the salary for year 25: The total money earned is the sum of an arithmetic series from year 1 to year 25. The sum of an arithmetic series is given by: Substitute , , and : After 25 years, Marquis will have earned a total of $1,805,000 from this job.