Find the final hourly wage if a $$ \$ 18.50 $$ starting wage is increased by $$ 2 \% $$ each year for 7 years The final hourly wage is $$ \$ \square $$ Round your answer to the nearest cent.

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UpStudy AI · Accepted Answer

To find the final hourly wage after a starting wage of $18.50 is increased by 2% each year for 7 years, we can use the formula for compound interest:

$$ A = P(1 + r)^n $$

where:
- $$ A $$ is the final amount (hourly wage in this case),
- $$ P $$ is the principal amount (starting wage of $18.50),
- $$ r $$ is the annual interest rate (2% in this case),
- $$ n $$ is the number of years (7 years in this case).

Given:
- Starting wage $$ P = \$18.50 $$
- Annual increase rate $$ r = 2\% = 0.02 $$
- Number of years $$ n = 7 $$

Substitute the values into the formula:

$$ A = 18.50(1 + 0.02)^7 $$

Now, we can calculate the final hourly wage using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$18.5\left(1+0.02\right)^{7}$$
- step1: Add the numbers:
  $$18.5\times 1.02^{7}$$
- step2: Convert the expressions:
  $$18.5\left(\frac{51}{50}\right)^{7}$$
- step3: Convert the expressions:
  $$\frac{37}{2}\left(\frac{51}{50}\right)^{7}$$
- step4: Multiply the numbers:
  $$\frac{37\times 51^{7}}{2\times 50^{7}}$$
The final hourly wage after a starting wage of $18.50 is increased by 2% each year for 7 years is approximately $21.25.

Rounded to the nearest cent, the final hourly wage is $21.25.
The final hourly wage is $21.25.

Find the final hourly wage if a \( \$ 18.50 \) starting wage is increased by \( 2 \% \) each year for 7 years The final hourly wage is \( \$ \square \) Round your answer to the nearest cent.

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