Justine earned $25,000 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.
geometric series
a = 25,000
r = 1.06
n = 5
sum = a (1-r^n)/(1-r)
= 25,000 ( -.338/-.06)
= (25,000)(5.637)
= $140,927.32
To find Justine's total earnings during the first five years on the job, we can use a formula for calculating compound interest. In this case, the principal amount is $25,000, the interest rate is 6%, and the compound period is 1 year.
After the first year, Justine's salary increases by 6%:
Total earnings in year 1 = $25,000
For the second year, her salary also increases by 6%:
Total earnings in year 2 = $25,000 + 6% of $25,000
For the third year:
Total earnings in year 3 = Total earnings in year 2 + 6% of Total earnings in year 2
And so on, until the fifth year.
Let's calculate it step-by-step:
Year 1:
Total earnings in year 1 = $25,000
Year 2:
Total earnings in year 2 = Total earnings in year 1 + 6% of Total earnings in year 1
= $25,000 + 0.06 * $25,000
= $25,000 + $1,500
= $26,500
Year 3:
Total earnings in year 3 = Total earnings in year 2 + 6% of Total earnings in year 2
= $26,500 + 0.06 * $26,500
= $26,500 + $1,590
= $28,090
Year 4:
Total earnings in year 4 = Total earnings in year 3 + 6% of Total earnings in year 3
= $28,090 + 0.06 * $28,090
= $28,090 + $1,685.4
= $29,775.4
Year 5:
Total earnings in year 5 = Total earnings in year 4 + 6% of Total earnings in year 4
= $29,775.4 + 0.06 * $29,775.4
= $29,775.4 + $1,786.524
= $31,561.92
Therefore, Justine's total earnings during the first five years on the job is $31,561.92.
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, we know that Justine earned $25,000 during the first year. To find her earnings for subsequent years, we need to apply the 6% raise to her salary each year.
The formula to calculate the raise amount is:
Raise Amount = (Percentage Raise / 100) * Previous Year's Earnings
In this case, the percentage raise is 6% and the previous year's earnings for the first year is $25,000. Using this formula, we can calculate her earnings for the second year:
Year 2 Earnings = $25,000 + (6% of $25,000)
To calculate the earnings for the third, fourth, and fifth year, we will use the same formula, but the previous year's earnings will be updated with the earnings from the previous year.
Year 3 Earnings = Year 2 Earnings + (6% of Year 2 Earnings)
Year 4 Earnings = Year 3 Earnings + (6% of Year 3 Earnings)
Year 5 Earnings = Year 4 Earnings + (6% of Year 4 Earnings)
Finally, to find the total earnings for the first five years, we simply add up the earnings for each year:
Total Earnings = Year 1 Earnings + Year 2 Earnings + Year 3 Earnings + Year 4 Earnings + Year 5 Earnings
Let's calculate it step by step:
Year 1 Earnings = $25,000
Year 2 Earnings = $25,000 + (6% of $25,000)
Year 3 Earnings = Year 2 Earnings + (6% of Year 2 Earnings)
Year 4 Earnings = Year 3 Earnings + (6% of Year 3 Earnings)
Year 5 Earnings = Year 4 Earnings + (6% of Year 4 Earnings)
Total Earnings = Year 1 Earnings + Year 2 Earnings + Year 3 Earnings + Year 4 Earnings + Year 5 Earnings
Let's calculate it now:
Year 1 Earnings = $25,000
Year 2 Earnings = $25,000 + (6% of $25,000)
Year 3 Earnings = Year 2 Earnings + (6% of Year 2 Earnings)
Year 4 Earnings = Year 3 Earnings + (6% of Year 3 Earnings)
Year 5 Earnings = Year 4 Earnings + (6% of Year 4 Earnings)
Year 2 Earnings = $25,000 + (0.06 * $25,000) = $25,000 + $1,500 = $26,500
Year 3 Earnings = $26,500 + (0.06 * $26,500) = $26,500 + $1,590 = $28,090
Year 4 Earnings = $28,090 + (0.06 * $28,090) = $28,090 + $1,685.4 = $29,775.4
Year 5 Earnings = $29,775.4 + (0.06 * $29,775.4) = $29,775.4 + $1,786.52 = $31,561.92
Total Earnings = $25,000 + $26,500 + $28,090 + $29,775.4 + $31,561.92 = $140,927.32
Therefore, Justine's total earnings during the first five years on the job amount to $140,927.32.