A man salary increase by $8000.00 every year. If his total at the end of 12years is 18,825,000.00
Find his initial salary
And after twelve years
Let's assume the man's initial salary is x.
After 12 years, we know that his total salary will be the sum of his initial salary and the increases over the 12 years.
So, the equation becomes:
x + 8000 + 8000 + 8000 +... (12 times) = 18,825,000
We can simplify this equation by realizing that the increases form an arithmetic sequence with a common difference of 8000. So, we can use the formula for the sum of an arithmetic sequence:
x + 8000(12) = 18,825,000
x + 96,000 = 18,825,000
x = 18,825,000 - 96,000
x = 18,729,000
Therefore, his initial salary is $18,729,000.
After twelve years, his salary will be his initial salary plus the total increases over the 12 years:
Salary after twelve years = 18,729,000 + 8000(12)
Salary after twelve years = 18,729,000 + 96,000
Salary after twelve years = $18,825,000.
To find the man's initial salary, we can use the formula for the arithmetic progression:
Sn = (n/2) * (2a + (n-1)d)
Where:
- Sn is the sum of the first n terms
- a is the first term
- d is the common difference between terms (the salary increase per year)
From the given information, we know:
- Sn = $18,825,000
- n = 12
- d = $8000
Plugging in these values, we can solve for a:
18,825,000 = (12/2) * (2a + (12-1) * 8000)
Simplifying further:
18,825,000 = 6 * (2a + 11 * 8000)
18,825,000 = 6 * (2a + 88,000)
18,825,000 = 12a + 528,000
12a = 18,825,000 - 528,000
12a = 18,297,000
a = 18,297,000 / 12
a ≈ $1,524,750
Therefore, the man's initial salary was approximately $1,524,750.
After twelve years, his salary can be determined by adding the yearly increase to his initial salary:
Initial Salary + (Number of years * Annual Increase)
≈ $1,524,750 + (12 * $8,000)
≈ $1,524,750 + $96,000
≈ $1,620,750
Therefore, after twelve years, his salary would be approximately $1,620,750.
To find the man's initial salary, we need to subtract the total salary increase over 12 years from the total amount at the end of 12 years.
Step 1: Calculate the total salary increase over 12 years.
Since the salary increases by $8000.00 every year, the total salary increase over 12 years would be $8000.00 multiplied by 12.
Total salary increase = $8000.00 * 12 = $96,000.00
Step 2: Subtract the total salary increase from the total amount at the end of 12 years to find the initial salary.
Initial salary = Total amount at the end of 12 years - Total salary increase
Initial salary = $18,825,000.00 - $96,000.00
Initial salary = $18,729,000.00
Therefore, the man's initial salary is $18,729,000.00.
After twelve years, the man's salary would be the total amount at the end of 12 years, which is $18,825,000.00.