Question

You are offered a job that pays $40,000 during the first year, with an annual increase of 5% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.05 times what it was in the previous year. What can you expect to earn in your fourth year on the job? Round your answer to the nearest dollar.

Answer 1

$46305

Step-by-step explanation:

First year pay = $40000

Rate of Increase = 5% per year after the first year

Second year pay = 40000(1.05)

To get the formula for subsequent years, we will use an exponential growth formula:

`\begin{gathered} y=a(1+r)^t \\ \text{where a = first year pay = \$40000} \\ r\text{ = 5\% = 0.05} \\ \sin ce\text{ we are starting the increase after year 1, time (t) in our formula: t - 1} \end{gathered}`
`\begin{gathered} \text{The function becomes:} \\ y=40000(1+0.05)^(t-1) \\ y\text{ = }40000(1.05)^(t-1) \end{gathered}`

in the fourth year: t = 4

`\begin{gathered} y=40000(1.05)^(4-1) \\ y=40000(1.05)^3 \\ y\text{ = \$46305} \end{gathered}`

You are expected to earn $46305 in your fourth year on the job