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Thread: 2U math help

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    2U math help

    2014 Mathematics 2U HSC paper, question 16 b):
    At the start of a month, Jo opens a bank account and makes a deposit of $500.
    At the start of each subsequent month, Jo makes a deposit which is 1% more
    than the previous deposit.
    At the end of every month, the bank pays interest of 0.3% (per month) on the
    balance of the account.
    (i) Explain why the balance of the account at the end of the second month is $500 (1.003)^2 + $500 (1.01) (1.003) .
    (ii) Find the balance of the account at the end of the 60th month, correct to
    the nearest dollar.

    I can do (i), but (ii) just looks so hard, because you have one number (1.01) increasing in power, but then (1.003) decreasing in power, it feels so complicated. Can someone explain this question as simple as possible?

  2. #2
    Senior Member integral95's Avatar
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    Re: 2U math help

    Well I hope you can see that



    You can take a factor of to get



    From there it's a sum of a geometric series with a ratio of
    “Smart people learn from their mistakes. But the real sharp ones learn from the mistakes of others.”
    ― Brandon Mull

  3. #3
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    Re: 2U math help

    omg I sort of get it now! how did you know to factorise that out to get that pattern???

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