suppose that an employee ears $28,000 in the first year on the job. Each year thereafter, the employee receives a %3 raise. Find the total amount that the employee earned in all 20 years.

so you have a GS where

a = 28000
r = .03
n = 20

you should know the formula for the sum of 20 terms of this GS

To find the total amount that the employee earned in all 20 years, we need to calculate the salary for each year and then sum them up.

First, let's find the salary for each year:

Year 1: $28,000 (given)
Year 2: $28,000 + 3% raise = $28,000 + ($28,000 * 3/100) = $28,000 + $840 = $28,840
Year 3: $28,840 + 3% raise = $28,840 + ($28,840 * 3/100) = $28,840 + $865.2 = $29,705.2
Year 4: $29,705.2 + 3% raise = $29,705.2 + ($29,705.2 * 3/100) = $29,705.2 + $891.16 = $30,596.36
...
Continuing this pattern, we can calculate the salary for each year.

Now, to find the total amount earned in all 20 years, we sum up the salaries for each year:

Total amount = Year 1 salary + Year 2 salary + Year 3 salary + ... + Year 20 salary

To make the calculation easier, we can use the formula for the sum of an arithmetic series:

Sum = (n/2) * (first term + last term)

In this case, n (the number of terms) is 20, the first term is $28,000, and the last term is the salary in the 20th year.

Now, let's calculate the salary for the 20th year:

Year 20: Salary = $28,000 * (1 + 3/100)^19 (using the compound interest formula)

To find the total amount, we plug in the values into the formula:

Total amount = (20/2) * ($28,000 + Salary in Year 20)

Now, let's calculate the salary in Year 20 and find the total amount earned:

Year 20: Salary = $28,000 * (1 + 3/100)^19
= $28,000 * (1.03)^19
= $28,000 * 1.71442486698
= $48,041.45 (rounded to two decimal places)

Total amount = (20/2) * ($28,000 + $48,041.45)
= 10 * ($28,000 + $48,041.45)
= 10 * $76,041.45
= $760,414.50

So, the total amount that the employee earned in all 20 years is $760,414.50.