A man gets a job with a salary of $40,000 a year. He is promised a $1900 raise each subsequent year. Find his total earnings for a 10-year period.
Total earnings for a 10-year period = $40,000 + ($1900 x 10) = $58,000
To find the man's total earnings for a 10-year period, we need to calculate his annual earnings for each of the 10 years and then sum them up.
Step 1: Calculate the annual earnings for each year using the given information.
Year 1: $40,000 (base salary)
Year 2: $40,000 (base salary) + $1,900 (raise) = $41,900
Year 3: $41,900 + $1,900 = $43,800
Year 4: $43,800 + $1,900 = $45,700
Year 5: $45,700 + $1,900 = $47,600
Year 6: $47,600 + $1,900 = $49,500
Year 7: $49,500 + $1,900 = $51,400
Year 8: $51,400 + $1,900 = $53,300
Year 9: $53,300 + $1,900 = $55,200
Year 10: $55,200 + $1,900 = $57,100
Step 2: Sum up the annual earnings for the 10-year period.
Total earnings = $40,000 + $41,900 + $43,800 + $45,700 + $47,600 + $49,500 + $51,400 + $53,300 + $55,200 + $57,100 = $486,500
Therefore, the man's total earnings for a 10-year period would be $486,500.
To find the man's total earnings for a 10-year period, we can use a simple mathematical formula.
First, we need to determine how much he earns each year. He starts with a salary of $40,000 and is promised a $1,900 raise each subsequent year. Therefore, his earnings for each year can be calculated as follows:
Year 1: $40,000
Year 2: $40,000 + $1,900
Year 3: $40,000 + 2 * $1,900 (since Year 2 includes the initial raise, and Year 3 should include two raises)
Year 4: $40,000 + 3 * $1,900
And so on...
We can observe that the earnings of each year form an arithmetic series, where the first term is $40,000 and the common difference is $1,900.
The formula for the sum of an arithmetic series is given by:
Sum = (n/2)(2a + (n-1)d)
Where:
- `Sum` is the total earnings
- `n` is the number of years (in this case, 10 years)
- `a` is the first term of the series ($40,000)
- `d` is the common difference ($1,900)
Using the formula, we can calculate the total earnings for a 10-year period:
Sum = (10/2)(2 * $40,000 + (10-1) * $1,900)
= 5 * ($80,000 + 9 * $1,900)
= 5 * ($80,000 + $17,100)
= 5 * $97,100
= $485,500
Therefore, the man's total earnings for a 10-year period would be $485,500.