Question

Job A offers to start new hires out at $25,000 with an 8% increase in salary per year. Job B offers to start a new hire off at $32,000 with a $1500 raise per year. Write an equation to model each job scenario, then use your equations to answer the following questions. Job type your answer... is the better offer initially, but after type your answer... years, Job type your answer... will pay $ type your answer... more per year than Job type your answer...

Answer 1

Given data:

The initial amount offer by Job A is P=$25,000.

The given rate of interest is r=8%.

The initial amount offer by job B is a=$32,000.

The given amount raise in job B is d= $1500.

The final salary in job A after t time is,

$\begin{gathered} A=P(1+\frac{r}{100})^t \\ =25,000(1+\frac{8}{100})^t \\ =25,000(1.08)^t \end{gathered}$

The final salary in job B after t time is,

$\begin{gathered} B=a+td \\ =32,000+t(1500) \\ =32,000+1500t \end{gathered}$

Evaluate the time at which both salaries are equal.

$\begin{gathered} 25,000(1.08)^t=32,000+1500t \\ 1.08^t=1.28+0.06t \\ t=6.805 \end{gathered}$