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Math Problem About Income

  1. Aug 22, 2009 #1
    How do you solve this?
    There is this kind of question in our test and I don't know how will I do it.

    You're working in a company. Your starting income is 5000. Every year, the income will increase by 5%. What is your total income on your 25th year in the company?
     
  2. jcsd
  3. Aug 22, 2009 #2

    HallsofIvy

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    This is a question, not a tutorial so I am moving out of "Learning Materials" to "Precalculus Homework and School Work".

    You startwith income at 5000 and it increases by 5% each year.

    Okay, the first year your increases by "5% of 5000"= .05(5000)= 250 so your income the second year is 5250= 5000+ (.05)5000= (1.05)(5000). At the end of that year it increases by "5% of 5250"= .05(5250)= 262.50 and the third year your income is 5512.50= 5250+ (.05)5250= (1.05)(5250)= 1.05(1.05(5000)). The reason I wrote it out like that is because neither you nor I want to do that 24 times! (During your 25th year, your income will have increased 24 times.) You should be able to see what is happening: each year your income is multiplied by 1.05. After 24 years, that initial 5000 is multiplied by 1.05 24 times: [itex](1.05)^{24}(5000)[/itex].
     
  4. Aug 22, 2009 #3
    [tex]a_1=5000[/tex]

    [tex]a_2=a_1+a_1*\frac{5}{100}=a_1*1.05[/tex]

    [tex]a_3=a_1*1.05 + a_1*1.05*0.05=a_1*1.05(1 + 0.05)=a_1*1.05*1.05[/tex]

    [tex]a_4=a_1*1.05*1.05*1.05[/tex]

    [tex]...................................[/tex]

    [tex]a_{n+1}=a_1*(1.05)^{n}[/tex]

    So a25=5000*(1.05)24

    Regards.
     
    Last edited: Aug 23, 2009
  5. Aug 22, 2009 #4
    Is 1.05 constant?
     
  6. Aug 23, 2009 #5
    Yep, its a constant.
     
  7. Aug 23, 2009 #6

    HallsofIvy

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    It's certainly not going to change!
     
  8. Aug 23, 2009 #7
    ok. where is that 1.05 come from?
     
  9. Aug 23, 2009 #8
    If you see my way of solving the problem, you'll spot that

    [tex]a_2=a_1+a_1*\frac{5}{100}=a_1(1+\frac{5}{100})=a_1\frac{100+5}{100}=a_1\frac{105}{100}=a_1*1.05[/tex]

    See now where it comes from?
     
  10. Aug 23, 2009 #9

    HallsofIvy

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    I thought I had said that. Each year, your income is the same as the previous year (100%) and an additional 5% raise. Together that means your income each year is 105% of the previous year's. 105% is the same as 1.05.
     
  11. Aug 24, 2009 #10
    If it helps anyone, you can work this sort of thing out on Calcatraz, my new online calculator.

    Just enter it as: http://www.calcatraz.com/calc?c=%245000+raised+by+5%25+in+year+25" [Broken], substituting your own values.
     
    Last edited by a moderator: May 4, 2017
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