Justine earned $30,000 during the first year of her job at city hall. After each year she received a 6% raise. Find her total earnings during the first five years on the job.
This is a geometric series with
a = 30000
r = 1.06
so you want:
30000 + 30000(1.06) + 30000(1.06)^2 + ... + 30000(1.06)^4
= 30000(1.06^5 - 1)/(1.06 - 1)
= 169112.79
To find Justine's total earnings during the first five years on the job, we need to calculate her earnings for each year and then sum them up.
First, let's calculate Justine's earnings for each year:
Year 1: $30,000
Year 2: $30,000 + 6% of $30,000
Year 3: Year 2 earnings + 6% of Year 2 earnings
Year 4: Year 3 earnings + 6% of Year 3 earnings
Year 5: Year 4 earnings + 6% of Year 4 earnings
Now, let's calculate her earnings for each year:
Year 2: $30,000 + (6/100) * $30,000 = $30,000 + $1,800 = $31,800
Year 3: $31,800 + (6/100) * $31,800 = $31,800 + $1,908 = $33,708
Year 4: $33,708 + (6/100) * $33,708 = $33,708 + $2,022.48 = $35,730.48
Year 5: $35,730.48 + (6/100) * $35,730.48 = $35,730.48 + $2,143.83 = $37,874.31
Finally, we sum up her earnings for the first five years:
Total earnings = Year 1 + Year 2 + Year 3 + Year 4 + Year 5
Total earnings = $30,000 + $31,800 + $33,708 + $35,730.48 + $37,874.31
Total earnings = $168,113.79
Therefore, Justine's total earnings during the first five years on the job would be $168,113.79.
To find Justine's total earnings during the first five years on the job, we need to calculate her earnings for each year and then sum them up.
To start, we have Justine's earnings in the first year, which is $30,000.
For the subsequent years, we need to calculate her earnings after each raise of 6%.
To find her earnings after the first year, we multiply her earnings from the previous year by 1.06 (1 + 6% expressed as a decimal). This will give us her new salary.
For example, to find her earnings in the second year, we calculate: $30,000 * 1.06 = $31,800.
To find her earnings in the third year, we calculate: $31,800 * 1.06 = $33,708.
We continue this process for each subsequent year.
Here's the breakdown for Justine's earnings during the first five years:
Year 1: $30,000
Year 2: $30,000 * 1.06 = $31,800
Year 3: $31,800 * 1.06 = $33,708
Year 4: $33,708 * 1.06 = $35,783.28
Year 5: $35,783.28 * 1.06 = $37,939.71
Finally, we sum up her earnings over the five years:
Total earnings = $30,000 + $31,800 + $33,708 + $35,783.28 + $37,939.71 = $169,231.99
Therefore, Justine's total earnings during the first five years on the job amount to approximately $169,231.99.