Question

mario got a new job with a starting salary of $48,000. if he gets a yearly raise of 2%, find marks salary after 30 years.

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth (in this case, salary growth with a percentage raise each year) is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal (initial amount), $r$ is the annual growth rate (as a decimal), and $t$ is the time in years.
Here, $P = 48000$, $r = 0.02$ (since 2% = 0.02), and $t = 30$.

Step2: Substitute the values into the formula

Substitute $P = 48000$, $r = 0.02$, and $t = 30$ into the formula $A = P(1 + r)^t$:
$$A = 48000(1 + 0.02)^{30}$$

Step3: Calculate $(1 + 0.02)^{30}$

First, calculate $(1.02)^{30}$. Using a calculator, $(1.02)^{30}\approx1.811361584$.

Step4: Calculate the final salary

Multiply this value by the initial salary:
$$A = 48000\times1.811361584\approx86945.356$$

Answer:

Approximately $\$86945.36$ (or depending on rounding, it could be presented as $\$86945$ or with more decimal places as needed. If we use more precise calculation for $(1.02)^{30}$, for example, using the formula for compound interest more accurately, the value is approximately $48000\times1.811361584 = 86945.356$, so we can round to two decimal places as $\$86945.36$)