Joshua Vermier of Sacramento, California, received a raise after his first year on the job to $45,800 from his initial salary of $44,000. What was Joshua's raise stated as a percentage? If inflation averaged 2.8 percent for the year, what was his real income after the raise? What was his real raise stated as a percentage?

4.09%, $44,552.53 and 1.26%

Explanation:

Given the following from the question:

Initial salary = IS = $44,000

New salary = NS = $45,800

Inflation = 2.8% = 0.028

To calculate Joshua's raise as a percentage, we employ the percentage change formula as follows:

Joshua's raise as a percentage = [ (NS - IS) : IS] * 100

= [ ($45,800 - $44,000) : $44,000] * 100

= [ ($1,800 : $44,000] * 100

= 0.0409 * 100

= 4.09%

To calculate Joshua's Real Income after the Raise, we employ the inflation adjusted income formula as follows:

Joshua's Real Income after the Raise = RNS = NS : (1 + Inflation Rate)

= $45,800 : (1 + 0.028)

= $45,800 : 1.028

= $44,552.53

To calculate Joshua's real raise as a percentage, we also employ the percentage change formula. The only difference is that we will now use the real income (RNS) of $44,552.53 to replace the nominal income (NS) of $45,800 as follows:

Joshua's real raise as a percentage = [ (RNS - IS) : IS] * 100

= [ ($44,552.53 - $44,000) : $44,000] * 100

= [ ($552.53 : $44,000] * 100

= 0.0126 * 100

= 1.26%