# Nia is trying to decide between two possible jobs. Job A pays \$2000 a month with a 2% annual raise.

Discussion in 'Calculator Requests' started by math_celebrity, Sep 29, 2018.

1. ### math_celebrityAdministratorStaff Member

Nia is trying to decide between two possible jobs. Job A pays \$2000 a month with a 2% annual raise. Job B pays 24,000 a year with a \$500 annual raise. Write a function to represent the annual salary for Job A after x years. Write a function to represent the annual salary for Job B after x years. After how many years would Nia have a greater salary at Job A?

Nia Job A salary at time t: S(t)
\$2,000 per month equals \$24,000 per year.
So we have S(t) = 24,000(1.o2)^t

Nia Job B salary at time t: S(t)
\$24,000 per year.
So we have S(t) = 24,000 + 500t

We want to know t when Job A salary is greater than Job B Salary:
24,000(1.o2)^t > 24,000 + 500t

Time | A | B
0 | 24000 | 24000
1 | 24480 | 24500
2 | 24969.6 | 25000
3 | 25468.99 | 25500
4 | 25978.37 | 26000
5 | 26497.94 | 26500
6 | 27027.9 | 27000
7 | 27568.46 | 27500
8 | 28119.83 | 28000
9 | 28682.22 | 28500
10 | 29255.87 | 29000
11 | 29840.98 | 29500
12 | 30437.8 | 30000
13 | 31046.56 | 30500