Problema Solution
After graduating college, you get two job offers, otherwise equal in every way:
$40,000 starting salary, with $2,000/year raises
$40,000 starting salary, with 4% annual raises
a) Find an equation for the salary at each job after t years
b) What would be your salary at each job after 5 years? 30 years?
c) Estimate when the jobs would have the same salary. Use any technique you'd like: tables, graphs, guess-and-check, etc.
Answer provided by our tutors
a) The salary for the first job after t years will be:
40,000 + 2,000t
The salary for the second job after t years will be:
40,000(1 + 0.04)^t
b) For t = 5 years we have:
First job salary: 40,000 + 2,000*5 = $50,000
Second job salary: 40,000(1 + 0.04)^5 = $48,666.12
For t = 30 years we have:
First job salary: 40,000 + 2,000*30 = $100,000
Second job salary: 40,000(1 + 0.04)^30 = $129,735.90
c)The jobs will have same salary when:
40,000 + 2,000t = 40,000(1 + 0.04)^t
1.04^t = 1 + t/20
For t = 1 year we have:
1.04^1 = 1.04
1 + 1/20 = 1.05
The jobs will have almost the same salary after 1 year.