Question 1140311
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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