I work as an English teacher at a charter school in Phoenix. One of my students asked me today how much an “A” would cost him, and all I told him was that he couldn’t afford it. Being an annoying little shit, he asked me for a dollar amount. I want to be able to tell him exactly how much it would cost. Unfortunately, I can’t remember a quick way to do this.
Let’s say I teach for 30 years at this school. We get a 10% total salary increase yearly (5% as a raise, 5% as a bonus). What is the formula to figure out how much I’ll make over the course of 30 years?
I know that the long way to do it is:
(S[sub]1[/sub])+(S[sub]1[/sub]*1.1)+(S[sub]2[/sub]*1.1). . .+(S[sub]29[/sub]*1.1)
Is there a shorter way to plug this in?
It’s been a LONG time since math class, but here’s my best guess at how to represent this as a series. I’m sure someone more apt at mathematics will be along shortly to correct me. 
s[sub]0[/sub] = your starting salary
30
Σ(s[sub]n-1[/sub] * 1.1)
n=1
Total amount earned = s[sub]0[/sub] + the summation.
Actually, that should be the summation to 29, not 30, I think. From the start of your career to the end of year 1, you’ll make s[sub]0[/sub]… likewise, from the start of year 29 to the beginning of year 30, you’ll make s[sub]29[/sub]
If your starting salary is s, the total you’ll earn is 10s*(1.1[sup]30[/sup] - 1).
Depends? Are youi in Mesa, Apache Junction, Gilbert, Tempe, Chandler, Ahwahtukee where?
I hear Kyrene School district pays quite well.
Just wondering, I’m developmentally mathematically Delayed so I can’t answer your exact Q. 
A lot less than you think.
My spirit guide tells me that you will be killed by a drunk driver, escaping from a domestic abuse scene, driving a white Ford Bronco (if that is any help). He will run the stop sign near the chain restaurant (Chili’s something like that…maybe Lone Star).
So stop worrying about the money and get on with the having fun.
Assuming 10% annual growth, you can simplify the formula so that total earnings over 30 years = year1 salary * 164.5. Your salary in year30 would be roughly 15.8 times the year1 salary.
It’s not 10%, it’s 5%. The bonus money isn’t a salary increase, and it isn’t compounded.
Money[Year x+1] = Salary[Year x+1] + Salary[Year x * .05]
Salary[Year x+1] = Salary[Year x * 1.05].
If Year 1 is $100,000, you get $105,000, salary for Year 2 goes $105,000.
Year 2 Money is the $105,000, plus a $5,250 bonus for $110,250.
Salary for Year 3 is a 5% raise, or $110,250.
Year 3 Money is the $110,250, plus a $5,512 bonus for $115,762.
etc…
Phlosphr, I’m in Phoenix itself, at a charter school.
muttrox, I realized that last night and figured it out. I just did it the long way and used Excel. I started with S[sub]0[/sub] of $36,000, and multiplied it by 1.05. After 30 years, my total earnings will be $2,556,388. I just calculated what each year’s bonus would be (S[sub]n-1[/sub]*0.05) and added the sum of those numbers on at the end.
So, in 30 years, I’ll still have made under $3M total. I’m kinda bummed about that. I am hopeful, however, that a student comes up with the cash for the A, so I can get out early!