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Math Help - AP/GP problem

  1. #1
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    Nov 2008
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    AP/GP problem

    Hi

    I'm having problems with part c of the question below

    http://stonehambey.com/Images/C2Q.png

    Because they're adding 1k every year and then the percentage interest is added (almost like a cross between an AP and a GP), it's left me feeling confused as how to solve it. I'm pretty sure I'm missing something obvious though

    Any pointers would be much appreciated

    Regards,

    Stonehambey
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Ap/gp

    Hello Stonehambey

    At the end of year 1, when the second payment of 1000 has been made, the first investment of 1000 will be worth 1000 \times 1.05. So the total amount in the savings account is now 1000 + 1000 \times 1.05 = 1000(1 + 1.05).

    At the end of year 2, when the third payment has just been made, the first investment is now worth 1000 \times 1.05^2 and the second payment is worth 1000 \times 1.05. So the total amount is now (1000 + 1000 \times 1.05 +  1000 \times 1.05^2) = 1000(1 + 1.05 + 1.05^2).

    At the end of year n, the total amount is 1000(1 + 1.05 + \dots ). Can you see what it will be?

    The series in the brackets is a GP, where the first term is ? and the common ratio is ? So what is the sum to n terms?

    Can you complete it now?

    Grandad
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