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Thread: Ncea Maths

  1. #1
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    Default Ncea Maths

    Here is a question form a NCEA Maths paper

    J has $5000 to invest for two and a half years
    Two schemes to choose from
    Scheme 1 - Invest the money in an account that pays 3.25% interest only at the end of each year
    Scheme 2 - Invest the money in an account that pays 1.3% interest at the end of each six months
    The question asked which would be the best scheme?

    Now ordinarily this is a easy question except that it is open to more than one interpretation My query is why do the people who set these questions not see the ambiguities.

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    Default Re: Ncea Maths

    This is the way that I would have worked it, given the information provided.

    Scheme One:
    3.25% of 5000 is 162.5
    This is interest for 1 year
    Multiply that by 2.5 and You get 406.25 in interest over 2.5 years.

    Scheme Two:
    1.3% of 5000 is 65
    This is interest for 0.5 of a year
    Multiply that by 5 and you get 325 interest in 2.5 years.

    Therefore scheme 1 would be better.

    It seemed fairly clear to me.

    Then again, I may have missed somthing.

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    Default Re: Ncea Maths

    Dally,
    I am assuming this question came from a Level 2 Maths paper. If so, the students are expected to be able to handle Compound Interest questions. It would seem to me to have come from a paper on Sequences and Series

    If that is the case, I would use the formula A = P(1 + r/100)^n . A is the final amount, P is the sum invested, r is the rate of interest in % and n is the number of interest periods.

    (a) If r = 3.25 % per year, n = 2.5 and I get A = $5416.21
    (b) If r = 1.3 % each 6 months, n = 5 and I get A = $5333.56

    I hope I haven't misinterpreted your question.

    Jim

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    Default Re: Ncea Maths

    IIRC, it was Level one, unless there was a similar question in that paper (i never remember the content of my exams )

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    6146-B Billy T's Avatar
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    Default Re: Ncea Maths

    Quote Originally Posted by Hhel View Post
    Dally,
    I am assuming this question came from a Level 2 Maths paper. If so, the students are expected to be able to handle Compound Interest questions. It would seem to me to have come from a paper on Sequences and Series

    If that is the case, I would use the formula A = P(1 + r/100)^n . A is the final amount, P is the sum invested, r is the rate of interest in % and n is the number of interest periods.

    (a) If r = 3.25 % per year, n = 2.5 and I get A = $5416.21
    (b) If r = 1.3 % each 6 months, n = 5 and I get A = $5333.56

    I hope I haven't misinterpreted your question.

    Jim
    I got the same results, assuming that the interest was compounding.

    Sherman appears to have assumed that it did not compound, but the real issue is whether or not any interest would be paid on the last six months of scheme 1, because the question clearly states that interest is paid only at the end of each year (the devil is in the detail).

    Since the term was ostensibly 2.5 years (early withdrawal), Option 1 would return just $5330.28 and the bank would get free use of the money for the last six months of the 30 month term. On that basis the second scheme would be ahead by $3.28 (whoopee do!)

    However, if the Bank ignored its "term" conditions and paid interest on the part year, then the first option would be better at $5416.89.

    Knowing Banks, the lender would probably be killed by a flying pig as they went to collect their ill-gotten capital gains.

    Yes indeed, ambiguity abounds!

    Cheers

    Billy 8-{)
    Last edited by Billy T; 13-12-2006 at 05:10 PM.
    Some days it's not even worth chewing through my restraints!

  6. #6
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    Default Re: Ncea Maths

    Scheme 1 (3.25%, paid anually):
    Start: $5000
    After 1 year, interest on $5000 is $162.50 (5000*0.0325), balance now $5162.50.
    After 2 years, interest on $5162.50 is $167.78 (5162.5*0.0325), balance now $5330.28.
    As the money is withdrawn before interest is paid on the third year, $5330.28 is the final balance.

    Scheme 2 (1.3%, paid bianually)
    Start: $5000
    After 6 months, interest on $5000 is $65 (5000*0.013), balance now $5065.
    After 12 months, interest on $5065 is $65.85 (5065*0.013), balance now $5130.85.
    After 18 months, interest on $5130.85 is $66.70 (5130.85*0.013), balance now $5197.55.
    After 24 months, interest on $5197.55 is $67.57 (5197.55*0.013), balance now $5265.12.
    After 30 months, interst on $5265.12 is $68.45 (5265.12*0.013(, balance now $5333.57.
    The money is withdrawn, $5333.57 is the final balance.

    Scheme 1 (3.25%): $5330.28
    Scheme 2 (1.30%): $5333.57
    Therefore scheme 2 is the better savings scheme.
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  7. #7
    Senior Member pctek's Avatar
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    Default Re: Ncea Maths

    I agree with Bletch.
    It states interest paid either after 1 year or interest paid after 6 months.

    So how is it open to interpretation?


    Most banks pay it monthly anyway....

  8. #8
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    Default Re: Ncea Maths

    NCEA sucks. That's all there is to it.
    Meh....

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    Default Re: Ncea Maths

    Quote Originally Posted by qazwsxokmijn View Post
    NCEA sucks. That's all there is to it.
    Too right.

    Quote Originally Posted by Bletch View Post
    Scheme 1 (3.25%, paid anually):
    Start: $5000
    After 1 year, interest on $5000 is $162.50 (5000*0.0325), balance now $5162.50.
    After 2 years, interest on $5162.50 is $167.78 (5162.5*0.0325), balance now $5330.28.
    As the money is withdrawn before interest is paid on the third year, $5330.28 is the final balance.

    Scheme 2 (1.3%, paid bianually)
    Start: $5000
    After 6 months, interest on $5000 is $65 (5000*0.013), balance now $5065.
    After 12 months, interest on $5065 is $65.85 (5065*0.013), balance now $5130.85.
    After 18 months, interest on $5130.85 is $66.70 (5130.85*0.013), balance now $5197.55.
    After 24 months, interest on $5197.55 is $67.57 (5197.55*0.013), balance now $5265.12.
    After 30 months, interst on $5265.12 is $68.45 (5265.12*0.013(, balance now $5333.57.
    The money is withdrawn, $5333.57 is the final balance.

    Scheme 1 (3.25%): $5330.28
    Scheme 2 (1.30%): $5333.57
    Therefore scheme 2 is the better savings scheme.
    Yip, I'd say this is the correct answer. I don't see how it's confusing... just read the question carefully and it's straight enough.

  10. #10
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    Default Re: Ncea Maths

    Thanks Billy - ambiguity does abound and it also does not state whether the investment is on call or term so Bletch if it is a term deposit and the money is withdraw after 2 years the interest is severely affected.

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