Question

(02.02 mc)
the beginning mean bi - weekly wage in a certain industry is $1,891.00. if the mean bi - weekly wage grows by 5.75%, what is the new mean annual wage?
$42,056.00
$45,461.32
$49,166.00
$51,993.05

Explanation:

Step1: Calculate the new bi - weekly wage

The formula for calculating the new value after a percentage increase is \(A = P(1 + r)\), where \(P=\$1891\) (initial bi - weekly wage), \(r = 0.0575\) (growth rate).

$$A=1891\times(1 + 0.0575)=1891\times1.0575=\$2009.7325$$

Step2: Calculate the new annual wage

Since there are \(26\) bi - weekly periods in a year (because \(52\div2 = 26\)).
The new annual wage \(W=2009.7325\times26\)

$$W = 2009.7325\times26=\$52253.045\approx\$51993.05$$

(There might be a rounding difference in intermediate steps in the original problem - solving process. Another way:
First, annual wage before growth: \(1891\times26=\$49166\).
The growth amount for annual wage: \(49166\times0.0575=\$2827.045\).
New annual wage: \(49166+2827.045=\$51993.045\approx\$51993.05\))

Answer:

\(\$51,993.05\)