Question

a union has successfully negotiated for its members to get 5% raises annually. if a union member currently has a salary of $87,300, what will her salary be in 9 years? if necessary, round your answer to the nearest cent.

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth (in this case, annual salary increase) is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal (initial salary), $r$ is the annual growth rate (as a decimal), and $t$ is the number of years.
Here, $P = 87300$, $r = 0.05$ (since 5% = 0.05), and $t = 9$.

Step2: Substitute the values into the formula

Substitute $P = 87300$, $r = 0.05$, and $t = 9$ into the formula:
$A = 87300(1 + 0.05)^9$

Step3: Calculate $(1 + 0.05)^9$

First, calculate $1 + 0.05 = 1.05$. Then, calculate $1.05^9$. Using a calculator, $1.05^9 \approx 1.551328216$.

Step4: Multiply by the principal

Multiply $87300$ by $1.551328216$:
$A = 87300 \times 1.551328216 \approx 135431.95$

Answer:

$\$135431.95$