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    kofigc's Avatar
    kofigc Posts: 21, Reputation: 1
    New Member
     
    #1

    Nov 3, 2010, 05:06 AM
    Further AP/GP Help Required
    Ok, so I have several questions on this topic area but am able to enter a number of answers for one question in particular yet achieve the same outcome (a score of 75%). This would suggest that the question I can enter several variations of answer for is incorrect, right?

    Please tell me what or where I'm going wrong with this if you know as it's driving me crazy!

    Question

    The value of a machine which costs £35000 has a costs of repairs and maintenance of £2000 in the first year and increases by 10% per year.
    After how many years will it be cheaper to buy a new machine than to pay for the repairs and maintenance up till then?

    I have tried using the following answers:

    31 years (2000 * 1.1^31 = £38388.68499)
    30 (30.04 rounded to nearest whole number as 2000*1.1^30.04 = £35032.10693)
    11 (using sum of geometric sequence S11 > £35000

    As I said earlier all of these give me a 75% scoring for the questions. HELP! :(




    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
    Uber Member
     
    #2

    Nov 3, 2010, 08:05 AM

    Unless I'm missing something...











    But since we want the year when it exceeds 35000, we take the nearest higher integer, which is 32 years.

    Replacing in the equation, we get:





    Hence, on the 31st year, it will still be cheaper to pay the repair and maintenance, but on the 32nd year, it's better to buy a new one.

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