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the starting salary for a job is $43,800 with a guaranteed increase of $1950 per hear Determine (a) the salary during the fifth year and the total compensation through five full years of employment

User Paul Houx
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Final answer:

The salary during the fifth year will be $51,600. The total compensation through five full years of employment will be $238,500. This problem is solved using the concept of an arithmetic sequence.

Step-by-step explanation:

The student is asking about the salary increment problem which can be solved using basic arithmetic sequences, a topic in mathematics. The starting salary for the job is $43,800, with an annual increase of $1,950.

Salary During the Fifth Year

To calculate the salary during the fifth year, we consider the yearly increase as a constant and add it to the starting salary for each of the first four years:

Salary in 5th year = Starting salary + 4 * Annual increase

Salary in 5th year = $43,800 + 4 * $1,950

Salary in 5th year = $43,800 + $7,800

Salary in 5th year = $51,600

Total Compensation Through Five Full Years

The total compensation over five years is the sum of the salaries for each year. This forms an arithmetic sequence where:

  • First term (a) = $43,800(the starting salary)
  • Common difference (d) = $1,950(the annual increase)
  • Number of terms (n) = 5

The formula for the sum of the first n terms of an arithmetic sequence is given by:

S_n = n/2 * [2a + (n-1)d]

Total compensation for 5 years (S_5) = 5/2 * [2*$43,800 + (5-1)*$1,950]

Total compensation for 5 years (S_5) = 5/2 * [$87,600 + $7,800]

Total compensation for 5 years (S_5) = 5/2 * $95,400

Total compensation for 5 years (S_5) = $238,500

User Myckhel
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