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Math Help - money and interest

  1. #1
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    Thumbs up money and interest

    the question says" when an amount is invested and compounded monthly, the amount is doubled after 10 years"
    a) identify a case where this would be true. stipulate the principle nad rate. prove.
    b) "this case is only true for one interest rate." explain mathematically if the statement is valid

    thank you for all your help i need it this arfternoon if possible thank you

    xxx
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  2. #2
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    sorry thats ment to say and not nad
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  3. #3
    Bar0n janvdl's Avatar
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    so P(1 + R)^t = 2P?

    lemme see.

    (1 + R)^10 = 2

    R = 10.root(2) - 1
    Thus R = 7.18% approx.
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  4. #4
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    Hello, mini!

    When an amount is invested and compounded monthly,
    the amount is doubled after 10 years.

    a) Identify a case where this would be true.
    Stipulate the principle and rate. .Prove.

    b) "This case is only true for one interest rate."
    Explain mathematically if the statement is valid.

    Use the compound interest formula: .A .= .P(1 + i)^
    n

    where: P = the principal invested
    . . . . . .i = periodic interest rate
    . . . . . n = the number of periods
    . . . . . A = the final amount of the investment


    We have P dollars invested at i percent per month for 120 months
    . . and its value grows to 2P.

    So we have: .P(1 + i)^
    120 .= .2P . . . . (1 + i)^120 .= .2

    Take the 120th root of both sides: .1 + i .= .(2)^
    1/120 .= .1.005792941

    Then: .i .= .0.005792941 .
    (monthly interest rate)


    Therefore, the annual interest rate is: .12 0.005792941 .= .0.069515293
    . . or about 7%.


    This is the only interest rate which satisfies the problem.
    . . (Note that the Principal does not matter.)

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  5. #5
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    thanks

    hi thanks for your answer but i aready handed the assignment in but i got it wrong thankyou for u help though it was much appreciated i might need it soe other time thanks
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  6. #6
    Bar0n janvdl's Avatar
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    Sorry i didnt see that the interest should be compounded monthly.
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