4. an employee starts a job with an annual salary of $30,000. each year they receive a 5% raise. what will…

4. an employee starts a job with an annual salary of $30,000. each year they receive a 5% raise. what will their salary be in the 5th year.

4. an employee starts a job with an annual salary of $30,000. each year they receive a 5% raise. what will their salary be in the 5th year.

Answer

Explanation:

Step1: Identify the formula for compound - growth

The formula for the salary $S$ after $n$ years with an initial salary $S_0$ and a growth rate $r$ is $S = S_0(1 + r)^n$. Here, $S_0=$30000$, $r = 0.05$, and $n = 4$ (because for the 5th - year salary, the number of growth periods is 4 starting from the first - year salary).

Step2: Substitute the values into the formula

$S=30000\times(1 + 0.05)^4$. First, calculate $(1 + 0.05)^4=1.05^4=1.05\times1.05\times1.05\times1.05 = 1.21550625$. Then, $S = 30000\times1.21550625=$36465.1875$.

Step3: Calculate the 5th - year salary

The 5th - year salary is $S_5=30000\times(1 + 0.05)^4\times(1 + 0.05)=30000\times(1.05)^5$. $(1.05)^5=1.05\times1.05\times1.05\times1.05\times1.05 = 1.27628$. $S_5=30000\times1.27628=$38288.4$. (The hand - written work has some calculation errors. The correct way is to use the compound - growth formula $S = S_0(1 + r)^n$ where $n$ is the number of years of growth. Starting from the first year, for the 5th year, $n = 4$ when calculating the growth from the initial salary. The correct answer using the formula $S=30000\times(1.05)^4=$36465.19$ (rounded to two decimal places) for the amount after 4 years of growth, and for the 5th year salary $S = 30000\times(1.05)^5=$38288.4$)

Answer:

$$38288.4$