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.

Question

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 starting wage is increased by each year for 7 years
The final hourly wage is
Round your answer to the nearest cent.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions

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