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One of the early questions in the NCEES FE Industrial/Systems Exam studyguide has a solution that I can't decipher. The question is as follows:

Bob wants to be a millionaire. To achieve this goal, at the end of the year he invests $5000 each year into an account that pays 10% interest, compounded yearly. How many years will it take Bob to reach this goal?

The part I need help with is the solution to this problem, it's in the image below within the red box. I have no idea how it gets from (5000)((1+0.1)^n - 1)/0.1) to 21 = 1.1^n. Can anyone provide an alternate solution or some explanation? Thank you!

enter image description here

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  • $\begingroup$ This is a maths question, not engineering. Wrong site. $\endgroup$ – Transistor Apr 1 at 12:42
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I'm not doing notation for this, it's simple algebra.

X = 1,000,000 = 5000 / .1 * ((1.1)^n - 1)

1,000,000 = 50,000(1.1)^n - 50,000

1,050,000 = 50,000(1.1^n)

divide both sides by 50,000

21 = 1.1^n

etc.

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