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Chapter 8: Problem 68

A company offers a starting yearly salary of \(\$ 33,000\) with raises of \(\$ 2500\) per year. Find the total salary over a ten-year period.

Short Answer

Expert verified
The total salary over a ten-year period is \($36750\).

Step by step solution

01

Determine the Yearly Salary

To find out how much the worker earns each year, one must first understand that for each year, the worker receives an additional $2500. Therefore, the salary for year n can be found using the formula \(Yearly Salary_{n} = 33000 + 2500 \cdot (n - 1) \) where \(n\) is between 1 and 10 (inclusive).
02

Sum up all Yearly Salaries

Next step is to sum up all these salaries to find the total amount earned over the ten-year period. This can be done using the following formula: \(Total Salary = \sum_ {n=1}^{10} (Yearly Salary_{n}) \). This is a sum of the yearly salaries from year 1 to year 10.
03

Compute the Total Salary

Finally, plug in the formula for Yearly Salary_{n} from Step 1 into the Total Salary formula in Step 2 and compute the result

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