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Math Help - arithmetic sequence

  1. #1
    Senior Member furor celtica's Avatar
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    arithmetic sequence

    sorry if im not posting this in the right place

    i though this would be pretty straightforward

    an employee starts work on an annual salary of $30 000. His pay scale will give him an increase of $800 per annum on 1 January until 1 January 2015 inclusive. He remains on this salary until he retires on 31 December 2040. How much will he earn during his working life?

    ok so the sum of the first 15 years is 0.5n(2a+d(n-1)) = 7.5 (60000 + 800 x 14) = 534 000
    his final salary l = a+d(n-1) = 41 200
    he will earn this every year for 25 years.
    so he will earn on total 534 000 + (41 200 x 25)
    =1 564 000

    this is wrong
    the real answer is $1 626 000
    how do i get to that? where is the mistake in my calculations?
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  2. #2
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    I don't understand how you got that answer. The one you claim is right.
    Judging by the data you gave.
    you're basically saying...

    He'd get 30k for 30 years.
    for 5 years he gets 800 per year.

    so it would be 900,000 + 4000 = 904,000.

    That is if you start from 2010
    You didn't mention a date you start from.
    I think this question is Missing something. Or maybe I'm miss understanding something.
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  3. #3
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    Quote Originally Posted by furor celtica View Post
    He remains on this salary until he retires on 31 December 2040.
    You're not giving a "start year": looks like it's year 2000;
    year 2000 to year 2040 = 41 working years, not 40.
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  4. #4
    Senior Member furor celtica's Avatar
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    yes sorry guys i forgot to include 1 January 2000 as starting date
    however, can you expand on your hint, can you show me in terms of my calculations?
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  5. #5
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    Quote Originally Posted by furor celtica View Post
    yes sorry guys i forgot to include 1 January 2000 as starting date
    however, can you expand on your hint, can you show me in terms of my calculations?
    YES...this means 16 years, final salary 42000....get it? WHY did you use 15 years?
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