If you plan to make an initial contribution of $6,000 to a retirement account in 5 years and you will make annual contributions of $6,000 thereafter, after how many contributions will your balance have reached at least $900,000 if your account earns 5.5% annual interest

Principles of Accounting Volume 2
19th Edition
ISBN:9781947172609
Author:OpenStax
Publisher:OpenStax
Chapter11: Capital Budgeting Decisions
Section: Chapter Questions
Problem 6MC: You want to invest $8,000 at an annual Interest rate of 8% that compounds annually for 12 years....
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If you plan to make an initial contribution of $6,000 to a retirement account in 5 years and you will make annual contributions of $6,000 thereafter, after how many contributions will your balance have reached at least $900,000 if your account earns 5.5% annual interest

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This helps ALOT but now I am confused how you got 41.55?  if I take 1.055 /9.25 =.11405 which if you move the decimal points gives you 40.5 or 41 but that is not making sense?  Sorry this is all new to me 

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I need to fill in the gap here and need this broken down a bit further

Where did the 9.25 come from?

Also, if 6000 x 1.055^n - 1 / .055 should equal 6000 (.055 /.055=1 x 6000).  How did you get 1.055^n?

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