Question 1140311: LaVonda is choosing between 2 jobs. For job A, she would earn $27,000 the first year and each year after that she would get a raise of $3,000. For Job B, she would earn $30,000 the first year and each year after that she would get a raise of 4% of the previous year’s salary. What is the first year during which LaVonda’s salary or job A would exceed that of Job B? Show your work, and explain the approach you used to find your answer. Which year would the total amount earned since starting Job A first exceed the total amount earned since starting job B? Show your work, and explain the approach you used to find your answer. Using sequence and series formulas, what would Lavonda’s yearly salary and total amount of money earned be after 20 years at Job A? What would her yearly salary and total amount of money earned be after 20 years at Job B? Show your work, and explain how you used the formulas to find your answer
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the formula used for job A is the arithmetic series formula is An = A1 + d * (n-1).
when A1 = 27000 and N = 20 and d = 3000, the formula becomes:
A20 = 27000 + 3000 * 19
solve for A20 to get 84,000.
the formula used for job B is the geometric series formula of An = A1 * r ^ (n-1).
when A1 = 30000 and n = 20 and r = 1.04, the formula becomes:
A20 = 30000 * (1.04) ^ 19 = 63205.47528.
to find out what year the salary of job A exceeds the salary of job B, you can use a process of elimination such as the one below.
you know that the increase in salary for job A is 3000 a year.
you know that the starting increase in salary for job B is 1200 a year.
in the second year on the job, salary for job A is 30000.
in the third year on the job, salary for job B is 33000.
in the second year on the job, salary for job B is 31200
in the third year on the job, salary for job B is about 32400.
it looks like salary for job A will overtake salary for job A somewhere around the third year on the job.
you can then use the formula to get the right year.
test for both in the third year on the job.
for job A, A3 = 27000 + 3000 * 2 = 33000
for job B, A3 = 30000 * 1.04 ^ 2 = 32448
job A salary is higher in the third year on the job.
test for both in the second year on the job.
for job A, A2 = 27000 + 3000 * 1 = 30000
for job B, A2 = 30000 * 1.04 ^ 1 = 31200
job B is still higher in year 2, but lower in year 3, so job A salary becomes higher than job B salary in the third year on the job.
the following excel spreadsheet shows the salaries based on the number of years on the job.
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