Bobby Joe is deciding between competing job offers. Offer A starts at $40,000 with a $2,000 raise every year. Offer B starts at $36,000 with a 6% raise each year. Which offer should Bobby Joe accept?

Answer 1

arithmetic sequence: after n years, with A he has earned 40n + n(n-1)

geometric sequence: after n years, with B he has earned 36 (1-1.06^n)/(1-1.06)

Using my graphing calculator, it will take 13 years before offer B will exceed offer A. So he should accept offer A.

Answer 2

A B

40000 36000

42000 38160

44000 40449.60

46000 42876.58

48000 45449.17

50000 48176.12

52000 51066.67

54000 54.130.70

If Bobby Joe intends on staying more than 7 years B is a better option.

Answer 3

Well, if money is the only reason then

it becomes a matter of TIME

40000 + 2000x = 36000 ( 1.06)^x

is the equation that will tell when they pay the same amount.

Rewriting: 36000 ( 1.06)^x - 2000x - 40000 = f(x) is a function of x

the solution is x=6.886

so after 6.886 years the first job shall pay 40000 + 6,886*2000 = 53772

and the second job shall pay 36000 * (1.06)^6.886 = 52772

Until that time, the first job pays more...

After that time, the second job pays more...