a job pays a salary of $19,00 the first year. during the next 10 years the salary increases by 4% each year. what is the lifetime salary over the 11 year period?

year 1 = 19000

year 2 = 19000(1.04)
year 3 = 19000(1.04)^2
..
year 10 = 19000(1.04)^9

I somehow expect that "they" want you to add them up.
It would be a GS, with a = 19000, r = 1.04 , n = 10

BUT, from an actuarial point of few monies cannot just be added up unless they are at the same spot on a time line.
I wonder if your question considers that.

geometric series

a + a r + a r^2 + a r^3 ... a r^10
a =19,000
r = 1.04

S = a (1-r^n)/(1-r)

Well, let's do some clown math here!

In the first year, the salary is $19,00. I'm assuming you meant $19,000 instead of $19,00? Moving on!

To find the lifetime salary over the 11-year period, we'll calculate the salary for each year and add them up.

For the first year, the salary is $19,000.

Then, for the next 10 years, the salary increases by 4% each year. Let me grab my clown calculator...

Year 2: $19,000 * 1.04 = $19,760
Year 3: $19,760 * 1.04 = $20,502.40
Year 4: $20,502.40 * 1.04 = $21,329.94
Year 5: $21,329.94 * 1.04 = $22,248.53
Year 6: $22,248.53 * 1.04 = $23,263.46
Year 7: $23,263.46 * 1.04 = $24,380.67
Year 8: $24,380.67 * 1.04 = $25,606.49
Year 9: $25,606.49 * 1.04 = $26,947.71
Year 10: $26,947.71 * 1.04 = $28,412.18
Year 11: $28,412.18 * 1.04 = $29,008.20

Now let's add up all those clown numbers!

$19,000 + $19,760 + $20,502.40 + $21,329.94 + $22,248.53 + $23,263.46 + $24,380.67 + $25,606.49 + $26,947.71 + $28,412.18 + $29,008.20 = $262,661.28

So, the lifetime salary over the 11-year period would be approximately $262,661.28. Keep in mind, this calculation assumes a 4% increase each year, so it's just a rough estimate. Happy clowning!

To calculate the lifetime salary over the 11-year period, we need to find the salary for each year and then sum them up.

Given:
Salary in the first year = $19,000
Salary increase by 4% each year for the next 10 years.

Step 1: Calculate the salary for each year.

First, let's calculate the increase in salary for each year using the formula for percentage increase:
Increase = Percentage increase in decimal form × Initial salary

Year 2: Increase = 4% × $19,000 = $760
Salary in year 2 = Initial salary + Increase = $19,000 + $760 = $19,760

Year 3: Increase = 4% × $19,760 ≈ $790.40
Salary in year 3 = $19,760 + $790.40 ≈ $20,550.40

Repeat this process for years 4-11.

Year 4: Increase ≈ $822.02, Salary ≈ $21,372.42
Year 5: Increase ≈ $855.30, Salary ≈ $22,227.72
Year 6: Increase ≈ $890.31, Salary ≈ $23,118.03
Year 7: Increase ≈ $927.03, Salary ≈ $24,045.06
Year 8: Increase ≈ $965.80, Salary ≈ $25,010.86
Year 9: Increase ≈ $1,006.43, Salary ≈ $26,017.29
Year 10: Increase ≈ $1,049.87, Salary ≈ $27,067.16
Year 11: Increase ≈ $1,095.88, Salary ≈ $28,163.03

Step 2: Sum up the salaries for each year.

Lifetime salary = Salary in year 1 + Salary in year 2 + ... + Salary in year 11

Lifetime salary ≈ $19,000 + $19,760 + $20,550.40 + $21,372.42 + $22,227.72 + $23,118.03 + $24,045.06 + $25,010.86 + $26,017.29 + $27,067.16 + $28,163.03

Calculating this sum will give you the lifetime salary over the 11-year period.

To find the lifetime salary over the 11-year period, we need to calculate the salary for each year and then add them together.

First, let's calculate the salary for each year, starting from the second year. We'll increase the previous year's salary by 4%.

Year 2 salary = $19,000 + (4% * $19,000) = $19,000 + $760 = $19,760
Year 3 salary = $19,760 + (4% * $19,760) = $19,760 + $790.4 = $20,550.40
Year 4 salary = $20,550.40 + (4% * $20,550.40) = $20,550.40 + $822.02 = $21,372.42
And so on, until the 11th year.

Now, let's calculate the salary for each year and add them together.

Year 1 salary = $19,000
Year 2 salary = $19,760
Year 3 salary = $20,550.40
Year 4 salary = $21,372.42
Year 5 salary = $22,227.79
Year 6 salary = $23,119.73
Year 7 salary = $24,050.70
Year 8 salary = $25,023.49
Year 9 salary = $26,041.22
Year 10 salary = $27,107.98
Year 11 salary = $28,228.83

Lifetime salary over the 11-year period = Sum of all salaries
= $19,000 + $19,760 + $20,550.40 + $21,372.42 + $22,227.79 + $23,119.73 + $24,050.70 + $25,023.49 + $26,041.22 + $27,107.98 + $28,228.83
= $258,832.06

Therefore, the lifetime salary over the 11-year period is $258,832.06.