Question

An applicant receives a job offer from two different companies. Offer A is a starting salary of $58,000 and a 3% increase for 5 years. Offer B is a starting salary of $56,000 and an increase of $3,000 per year. Which offer will provide a greater total income after 5 years? Show all necessary math work.

Answer 1

offer B will provide a greater total after 5 years.

Step-by-step explanation:

Offer A:

starting salary = $58000

rate of increase = 3% = 0.03

time = 5 years

This is an exponential function. The total becomes:

`\begin{gathered} f(x)=a(1+r)^t \\ \text{the total = starting salary (1+ rate of increase)}^(time) \\ \text{total = 58000 (1 + }0.03)^5 \end{gathered}`

Offer B:

starting salary = $56000

increase per year = $3000

This is a linear function. The total becomes:

`\begin{gathered} y\text{ = mx + b} \\ m\text{ = rate, b = starting salary},\text{ x = number of years} \\ \text{The total becomes:} \\ \text{Total = starting salary + increase(number of years)} \\ \text{Total = 56000 + 3000(x)} \end{gathered}`

For time = 5 years:

`\begin{gathered} \text{offer A: total = 58000(1+0.03)}^5 \\ \text{total = 58000(1.03)}^5\text{ = 67237.8}963 \\ \text{Total = \$67237.90} \\ \\ \text{offerr B: total = 56000 + 3000(5)} \\ \text{total = 56000 + 15000} \\ \text{Total = \$71000} \end{gathered}`

$71000 is greater than $67237.90.

Hence, offer B will provide a greater total after 5 years.