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Math Help - Interest Comparisons

  1. #1
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    Interest Comparisons

    I have 2 questions which are stumping me.
    1)
    Which simple interest rate is equal to the annual continuous interest
    rate 8% if a certain amount of money is invested for 4 years?
    Im having a problem with this one when it comes to the time of money invested. I cannot seem to incorporate this into my solution.


    2)Which is rate would be preferred?
    Two credit card companies offer 2 different rates for outstanding balance.
    1.75% per month.
    5.3% quarterly.
    By looking at this question I am leaning towards 5.3% quarterly, but I cannot prove it.

    Thanks in advance for any help
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  2. #2
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    Quote Originally Posted by MatsSundin View Post
    I have 2 questions which are stumping me.
    1)
    Which simple interest rate is equal to the annual continuous interest
    rate 8% if a certain amount of money is invested for 4 years?
    Im having a problem with this one when it comes to the time of money invested. I cannot seem to incorporate this into my solution.


    2)Which is rate would be preferred?
    Two credit card companies offer 2 different rates for outstanding balance.
    1.75% per month.
    5.3% quarterly.
    By looking at this question I am leaning towards 5.3% quarterly, but I cannot prove it.

    Thanks in advance for any help
    Investing your hockey money after retiring, Mats?

    1st question: clarify simple interest; no compounding at any time?

    2nd question:
    1.075^12 = 1.2314....23.14%
    1.053^4 = 1.2294.....22.94%
    Purty close...both Shylocks
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  3. #3
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    Thanks for the response, I figured I would want to make the right decision with my millions, might as well do something right since I couldn't win a cup in Toronto
    Anyway, I appreciate your response on the questions. And to clarify I am pretty sure question 1 is implying basic simple interest with a compound each year. A=P(1+rt). I have tried to convert this using Effective rate of interest for compounding interest
    Reff=((1+r/n)^n)-1
    and Effective rate of interest for continuously compounded interest
    Reff=(e^r)-1

    neither of these equations incorporate the fact that the investment was for a total of 4 years, telling me this is not the way to go. Any help is appreciated thank you.
    Last edited by MatsSundin; October 2nd 2009 at 05:45 AM. Reason: typos
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  4. #4
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    I think I have figured it out if anyone is interested.
    By setting both interest rate formulas equal to each other you can solve for r*

    P(1+tr*)=Pe^rt
    P's cancel leaving
    (1+4r*)=e^(.32) after substitutions
    r*=0.0943
    r*=9.43%

    Thanks for all the help
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  5. #5
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    Don't they have an Old Men's Hockey League in Sweden?

    OK; cpd continuous after 4 years:
    e^(.08 * 4) = 1.3771... a dollar is worth ~1.38

    Because of the "4 years" being specified, I'm pretty sure the question
    means NO compounding at any time:
    the the annual non-cpd rate is simply .3771 / 4 = .094275; ~9.43%

    But if we use cpd annually then:
    (1 + i)^4 = 1.3771
    i = 1.3771^(1/4) - 1 = .08328....; ~8.33%

    EDIT: I see you got it...

    But you get same results after 1 year cpd continuous:
    e^(.08) = 1.08328

    So they must mean SIMPLE SIMPLE SIMPLE.... interest.

    Investing your $10 million:
    8% continuous: interest 4 years = 3,771,277
    8% truly simple:interest 4 years = 3,200,000
    Difference: 571,277
    I'll take half as your investing agent...
    May I have an advance...NOW?

    EDIT: I see you got it!
    Last edited by Wilmer; October 2nd 2009 at 07:55 AM. Reason: add note
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