A job pays a salary of $25,000 the first year. During the next 22 years, the salary increases by 6% each year. What is the total lifetime salary over the 23-year period?

Question

anonymous · Answer

$$tls = 25000(1.06)^{y-1}$$

anonymous · Answer

so, when y=1, after the first year, he makes a salary of $25000. After that, his salary compounds at a rate of 6% per year, until y=23.

anonymous · Answer

Also, remember that this equation calculates what his final salary is; not what he made over a 23 year period, lol

anonymous · Answer

Maybe it would be better too look at it this way:

"During"  year 1:
$$salary = 25000 *1.06^{1-1} = 25000*1 = $25000$$

Salary during year 2:
$$salary = 25000*1.06^{2-1} = 25000*1.06$$

Salary during year 3:
$$salary = 25000*1.06^{3-1} = 25000*1.06*1.06$$

Salary during year 4:
$$salary = 25000*1.06^{4-1} = 25000*1.06*1.06*1.06$$

...Until year 23, when you have multiplied the salary the individual received during his first year of 25000 buy 1.06 (or an increase of 6%) 22 times for each year his salary increases.

The final amount is approximately:
$90, 088.44

anonymous · Answer

Thank you for your help. I was in the process of working it once my Aunt showed me how to do it, and I got the same thing. Thank you so much!