A company is offering a job with a salary of 48000 and a raise of 2 percent each year. Write a formula to represent the salary after each year then determine after 30 years.
Salary compound annually.
P = Po(1+r)^n.
Po = Initial pay.
n = the number of compounding periods.
P = 48,000(1.02)^30.
To determine the salary after each year, we can use the following formula:
Salary after each year = Initial salary * (1 + raise percentage)
Here, the initial salary is $48,000, and the raise percentage is 2%.
Therefore, the formula becomes:
Salary after each year = $48,000 * (1 + 0.02)
To calculate the salary after 30 years, we need to calculate the salary for each year and accumulate it. Here's the step-by-step calculation:
1. Calculate the salary after the first year:
Salary after the first year = $48,000 * (1 + 0.02) = $48,960
2. Calculate the salary after the second year:
Salary after the second year = $48,960 * (1 + 0.02) = $49,920
3. Calculate the salary after the third year:
Salary after the third year = $49,920 * (1 + 0.02) = $50,880
4. Repeat this calculation for all 30 years, accumulating the salary each year.
After calculating the salary for 30 years, the final result will be the salary after 30 years.
To represent the salary after each year with a 2 percent raise, you can use the following formula:
Salary after n years = Initial salary * (1 + (raise rate/100))^n
In the given scenario, the initial salary is $48,000, and the raise rate is 2 percent or 0.02.
Using the formula, we can determine the salary after 30 years:
Salary after 30 years = $48,000 * (1 + (0.02))^30
Now, let's calculate the result step by step:
Raise rate = 0.02
Initial salary = $48,000
Number of years = 30
Salary after 30 years = $48,000 * (1 + 0.02)^30
Using a calculator, we can simplify this:
Salary after 30 years ≈ $48,000 * (1.02)^30
≈ $48,000 * 1.718281828459045^30
≈ $48,000 * 1.811874689966276
≈ $87,014.87 (rounded to two decimal places)
Therefore, after 30 years, the salary would be approximately $87,014.87.