Question

Ashley took a job with a starting salary of $40,000 and can expect a 6% raise in pay each year. After 6.959 years, she would be earning $60,000 per year. Confirm this result algebraically.

A. $40,000 * (1 + 0.06)^6.959 = $60,000
B. $40,000 + 0.06 * 6.959 = $60,000
C. $40,000 / (1 + 0.06)^6.959 = $60,000
D. $40,000 * (1 - 0.06)^6.959 = $60,000

Answer 1

To confirm Ashley's salary after 6.959 years with a 6% annual raise, you use the exponential growth formula, and the correct option is A. $40,000 × (1 + 0.06)^6.959. Using a calculator, we can compute the raise to see if it equals $60,000.

Step-by-step explanation:

To confirm algebraically if Ashley's salary will reach $60,000 after 6.959 years with an annual raise of 6%, you would need to apply the formula for exponential growth which is:

Final Salary = Initial Salary × (1 + Growth Rate)^Years

In this case, the correct formula from the given options is:

A. $40,000 × (1 + 0.06)^6.959 = $60,000

Let's calculate:

Final Salary = $40,000 × (1 + 0.06)^6.959

Final Salary = $40,000 × (1.06)^6.959

We can use a calculator to find the value of (1.06)^6.959 and then multiply it by $40,000.

If the result is equal to $60,000, then option A confirms that Ashley would be earning $60,000 after 6.959 years.