a job pays a salary of 18,000 the first year. during the next 18 years,the salary increases 7% each year.what is the total lifetime salary over 19 years
18,000 * 1.07^18
To calculate the total lifetime salary over 19 years, we need to calculate the salary for each year and then sum them up.
The salary for the first year is given as $18,000. From the second year onward, the salary increases by 7% each year.
To calculate the salary for a specific year, we can use the formula:
Salary for a specific year = Salary for the previous year + (Salary for the previous year * 7%)
Let's calculate the salary for each year and sum them up over 19 years:
Year 1: $18,000
Year 2: $18,000 + ($18,000 * 7%) = $18,000 + ($18,000 * 0.07) = $18,000 + $1,260 = $19,260
Year 3: $19,260 + ($19,260 * 7%) = $19,260 + ($19,260 * 0.07) = $19,260 + $1,348.20 = $20,608.20
We can continue this calculation for each year until Year 19. However, to simplify the process, we can use a geometric series formula to find the sum of all 19 years' salaries.
Sum of a geometric series = a * (1 - r^n) / (1 - r)
Here, a = $18,000 (the first year's salary)
r = 1 + 7% = 1 + 0.07 = 1.07 (the common ratio)
n = 19 (the number of years)
Let's calculate the sum:
Sum = $18,000 * (1 - 1.07^19) / (1 - 1.07)
Calculating this expression will give us the total lifetime salary over 19 years.
To calculate the total lifetime salary over 19 years, we need to find the sum of all the yearly salaries.
Step 1: Calculate the salary for each year after the first year.
The salary for the second year is obtained by increasing the salary of the first year by 7%:
Salary for the second year = Salary of the first year + (7% of Salary of the first year)
= 18,000 + (0.07 * 18,000)
= 18,000 + 1,260
= 19,260
Similarly, we can calculate the salary for each of the subsequent years.
Step 2: Find the total salary for the remaining 18 years.
To calculate the total salary for the remaining 18 years, we need to sum up the salaries for each year.
Total salary for the remaining 18 years = Salary for the second year + Salary for the third year + ... + Salary for the nineteenth year
Using the same logic, we can calculate the salaries for the other 17 years and sum them up.
Total salary for the remaining 18 years = 19,260 + (1.07 * 19,260) + (1.07^2 * 19,260) + ... + (1.07^17 * 19,260)
Step 3: Calculate the total lifetime salary.
The total lifetime salary over 19 years can be found by adding the salary of the first year to the total salary for the remaining 18 years.
Total lifetime salary = Salary of the first year + Total salary for the remaining 18 years
Remember that the salary of the first year is given as $18,000.
Total lifetime salary = 18,000 + Total salary for the remaining 18 years
Now, let's calculate the total salary for the remaining 18 years and then add it to the initial salary of $18,000.
Total salary for the remaining 18 years = 19,260 + (1.07 * 19,260) + (1.07^2 * 19,260) + ... + (1.07^17 * 19,260)
To find the total lifetime salary, calculate the above expression.