Problem 68

Question

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.

Step-by-Step Solution

Verified
Answer
The total salary over a ten-year period is \($36750\).
1Step 1: 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).
2Step 2: 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.
3Step 3: 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