A job pays a salary of 35,000 the first year. During the next 10 years, the salary increases by 4% each year. What is the salary for the 11th year? What is the total salary over the 11 year period? (Round to the nearest cent.)
salary 1st year = 35000
salary 2nd year = 35000(1.04)
salary 3rd year = 35000(1.04)^2
...
salary 11th year = 3500(1.04)^10 = 51,808.55
sum of 11 terms of this GS
a = 35000
r = 1.04
sum(11) = a(r^11 - 1)/(r-1)
= 35000( 1.04^11 - 1)/(1.04 - 1) = 472,022.30
To find the salary for the 11th year, we need to calculate the increase in salary for each year from the 2nd to the 11th year.
First, let's find the salary for the 2nd year:
Salary for the 2nd year = Salary for the 1st year + (4% of the salary for the 1st year)
= $35,000 + (0.04 × $35,000)
= $35,000 + $1,400
= $36,400
Now, let's find the salary for the 3rd year:
Salary for the 3rd year = Salary for the 2nd year + (4% of the salary for the 2nd year)
= $36,400 + (0.04 × $36,400)
= $36,400 + $1,456
= $37,856
We can continue this calculation for each year to find the salary for the 11th year.
Salary for the 4th year = $39,314.24
Salary for the 5th year = $40,795.40
Salary for the 6th year = $42,302.98
Salary for the 7th year = $43,838.76
Salary for the 8th year = $45,404.43
Salary for the 9th year = $46,801.95
Salary for the 10th year = $48,711.63
Salary for the 11th year = $50,680.94
The salary for the 11th year is $50,680.94.
To find the total salary over the 11-year period, we can add up all the salaries from the 1st to the 11th year:
Total Salary = Salary for the 1st year + Salary for the 2nd year + ... + Salary for the 11th year
Total Salary = $35,000 + $36,400 + $37,856 + ... + $50,680.94
Total Salary ≈ $444,667.36
Therefore, the total salary over the 11-year period is approximately $444,667.36.
To find the salary for the 11th year, we need to calculate the salary increase for each of the 10 years and add it to the initial salary.
Step 1: Calculate the salary increase for each year.
The salary increases by 4% each year, which means it increases by 4% of the previous year's salary. To calculate the salary increase for each year, we multiply the previous year's salary by 4% (0.04).
Year 1: $35,000 (initial salary)
Year 2: $35,000 + ($35,000 * 0.04)
Year 3: $35,000 + ($35,000 * 0.04) + (($35,000 + ($35,000 * 0.04)) * 0.04)
...
Year 11: $35,000 + (salary increase each year for the previous 10 years)
Step 2: Calculate the salary for the 11th year.
To find the salary for the 11th year, we need to find the sum of the initial salary and the salary increase for each of the previous 10 years.
Salary for the 11th year = $35,000 + (salary increase each year for the previous 10 years)
Step 3: Calculate the total salary over the 11 year period.
To find the total salary over the 11 year period, we need to calculate the sum of the salaries for each of the 11 years.
Total salary over the 11 year period = Sum of the salaries for Year 1 to Year 11
Note: Given that the salary increase is constant each year, there is a formula to directly calculate the total salary over the specified period, but I will explain the step-by-step method for better understanding.
Let's calculate the values step-by-step:
Step 1: Calculate the salary increase for each year:
Year 1: $35,000
Year 2: $35,000 * 0.04 = $1,400
Year 3: ($35,000 + $1,400) * 0.04 = $1,416
Year 4: ($35,000 + $1,400 + $1,416) * 0.04 = $1,431.84
Year 5: ($35,000 + $1,400 + $1,416 + $1,431.84) * 0.04 = $1,447.27
Year 6: ($35,000 + $1,400 + $1,416 + $1,431.84 + $1,447.27) * 0.04 = $1,463.20
Year 7: ($35,000 + $1,400 + $1,416 + $1,431.84 + $1,447.27 + $1,463.20) * 0.04 = $1,479.64
Year 8: ($35,000 + $1,400 + $1,416 + $1,431.84 + $1,447.27 + $1,463.20 + $1,479.64) * 0.04 = $1,496.59
Year 9: ($35,000 + $1,400 + $1,416 + $1,431.84 + $1,447.27 + $1,463.20 + $1,479.64 + $1,496.59) * 0.04 = $1,514.06
Year 10: ($35,000 + $1,400 + $1,416 + $1,431.84 + $1,447.27 + $1,463.20 + $1,479.64 + $1,496.59 + $1,514.06) * 0.04 = $1,532.05
Step 2: Calculate the salary for the 11th year:
Salary for the 11th year = $35,000 + ($1,400 + $1,416 + $1,431.84 + $1,447.27 + $1,463.20 + $1,479.64 + $1,496.59 + $1,514.06 + $1,532.05)
Step 3: Calculate the total salary over the 11 year period:
Total salary over the 11 year period = $35,000 + ($35,000 * 0.04) + ($35,000 + $1,400) * 0.04 + ... + Salary for the 11th year.
Calculating the values using these steps, the salary for the 11th year is $42,011.65 (rounded to the nearest cent), and the total salary over the 11-year period is $515,673.38 (rounded to the nearest cent).