You are investigating two employment opportunities Company A

You are investigating two employment opportunities. Company A offers $30,000 the first year. During the next four years, the salary is guaranteed to increase by 6% per year. Company B offers $32,000 the first year, with guaranteed annual increases of 3% per year after that. Which company offers the better total salary for a five-year contract? By how much? Round to the nearest dollar.

Solution

The function for salary can be modelled in terms of an expeonential function:

Salary(t) = So(1+r)^t

where r increase factor and t is time

Company A :

Sa = 30000( 1+0.06)^t = 30000(1.06)^t

Compny B

Sb = 32000(1+0.03)^t = 32000(1.03)^t

Aftre t= 5 ; Sa = 30000(1.06)^5 = $40146.76 = $40147

Sb = 32000(1.03)^5 = $ 37096.77 = $37097

So, we can see after five years salary of company A is more than company B by $ 3050