Rena has been offered entry-level positions with two firms.

Question

Firm A offers a starting salary of $40 000 per year, with a $2000 per year increase guaranteed each subsequent year.
Firm B offers a starting salary of $38 500, with a 5% increase every year after that.

a)After how many years will Rena earn the same amount at each firm?
b) At which firm will Rena earn more after
i) 10 years ii) 20 years

Answer 1

Firm A's salaries increase linearly, (they form an arithmetic sequence)
Firm B;s salaries increase exponentially, (they form a geometric sequence)

SA = 2000t + 40000, where t is number of years after starting
SB = 38500(1.05)^t

a) you would have to solve
38500(1.05^t = 40000 + 2000t
385(1.05)^t = 400 + 20t

I would just try a few values of t

t Left-side RS
5 491 500
8 569 560
7 542 540
9 597 580

What is your conclusion?

for b) just sub t = 10 and t = 20 into both equations.