Answer:
about 55.8
Explanation:
The salary multiplier each year is 1.0125, so after n years, the salary has been multiplied by 1.0125^n.
We want to find the value of n that makes this multiplier be 2.
2 = 1.0125^n
log(2) = n·log(1.0125) . . . . . . . . . taking logs makes this a linear equation
n = log(2)/log(1.0125) ≈ 55.8
The model predicts 55.8 years will go by until you are making $100,000.
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More explanation of the factors used above
When 1.25% of s is added to s, the total is ...
s + .0125s = s(1 +.0125) = 1.0125s . . . . . . the multiplier is 1.0125
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After 2 years, the salary will be ...
(s·1.0125)·1.0125 = s·1.0125²
After 3 years, the salary will be ...
(s·1.0125²)·1.0125 = s·1.0125³
After n years, the salary will be ...
s·1.0125^n
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Estimate/Reasonableness check
The "rule of 72" tells you the doubling time in years is approximately 72/(annual percentage). For percentage = 1.25, this is ...
doubling time ≈ 72/1.25 = 57.6 . . . years
This is in the neighborhood of the answer we calculated, so we conclude our answer is correct.