1) Janet is offered a job with a starting salary of $15,000, and a guaranteed annual increase of $600. If she takes the job, what will be her guaranteed salary for the 10th year? What would her total earnings be for the first 10 years?
Answer: $21,000 ; $ 198,000
2) Sue's aunt wills her money for as long as she stays in school. The first year she is to get $1500, and each year after she gets $300 more than in the preceding year. How much money will she get altogether if she stays in school for 8 years?
Answer: $24,300
Are my answers correct?
15000+9*600 = 20400
At the start of the 10th year, she has had only 9 increases.
10/2 (15000+20400) = 177000
8/2 (2*1500 + 7*300) = 20400
Looks like a small review of A.P.'s is in order.
1) Yes, your answer is correct.
To calculate Janet's guaranteed salary for the 10th year, you start with her starting salary of $15,000 and then add the annual increase of $600 for each year. So for the 10th year, you can calculate it as follows:
Starting salary: $15,000
Annual increase: $600
Her salary for the 10th year will be the starting salary plus the annual increase multiplied by the number of years. In this case, it will be:
$15,000 + ($600 x 9) = $15,000 + $5,400 = $21,000
So her guaranteed salary for the 10th year will be $21,000.
To calculate her total earnings for the first 10 years, you need to sum up her guaranteed salary for each year. In this case, it will be:
Starting salary: $15,000
Annual increase: $600
Number of years: 10
Total earnings = (Starting salary + (Annual increase x (Number of years - 1))) x Number of years
= ($15,000 + ($600 x 9)) x 10
= ($15,000 + $5,400) x 10
= $21,000 x 10
= $210,000
So her total earnings for the first 10 years will be $210,000.
2) No, your answer is incorrect.
To calculate Sue's total money if she stays in school for 8 years, you start with her first-year amount and then increment it by $300 each year. So the total can be calculated as follows:
First-year amount: $1,500
Annual increase: $300
Number of years: 8
To find the total amount, you add up the series of amounts for each year. You can use the formula for the sum of an arithmetic series to calculate it:
Total amount = (n/2) * (2a + (n-1)d)
Where:
n - number of terms (in this case, number of years)
a - first term (first-year amount)
d - common difference (annual increase)
Using the formula, you can calculate Sue's total amount as:
Total amount = (8/2) * (2 * $1,500 + (8-1) * $300)
= 4 * ($3,000 + 7 * $300)
= 4 * ($3,000 + $2,100)
= 4 * $5,100
= $20,400
So if Sue stays in school for 8 years, she will get a total of $20,400.