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Math Help - compound interest? help please

  1. #1
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    compound interest? help please

    can anyone help me with a formula for this?
    What interest rate is required to earn $250 interest on a $999 investment over 3 years compounding daily

    Thank You
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  2. #2
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    Quote Originally Posted by xxpink__saltxx View Post
    can anyone help me with a formula for this?
    What interest rate is required to earn $250 interest on a $999 investment over 3 years compounding daily

    Thank You
    999=250\times i^x where i is interest (plus 1) and x is the number of time periods.

    So how many days are in 3 years, let's assume there's no leap-year. The answer is 1095 days

    So: 999=250\times i^{1095}

    Thus: \frac{999}{250}=i^{1095}

    Then: \sqrt[1095]{\frac{999}{250}}=i\approx 1.00126591

    So interest is: \approx .126591\%
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  3. #3
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    Hello, xxpink__saltxx!

    What interest rate is required to earn $250 interest on a $999 investment
    over 3 years compounding daily?

    The compound interest formula is: . A \;= \;P(1 + i)^n

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


    We are given: . A = 999,\;P = 250

    Since the interest is compounded daily, the interest rate is: \frac{I}{365}
    . . and the number of periods is: 3 \times 365 \,=\,1095

    So we have: . 999 \;=\;250\left(1 + \frac{I}{365}\right)^{1095}
    . . and we must solve for I, the annual interest rate.


    We have: . \left(1 + \frac{I}{365}\right)^{1095} \:=\:\frac{999}{250} \:=\:3.996

    Raise both sides to the \frac{1}{1095} power:
    . . \left[\left(1 + \frac{I}{365}\right)^{1095}\right]^{\frac{1}{1095}} \;=\;(3.996)^{\frac{1}{1095}} \quad\Rightarrow\quad 1 + \frac{I}{365}\:=\:1.001265909

    . . Then: . \frac{I}{365}\:=\:0.001265909\quad\Rightarrow\quad I \:=\;0.462056836

    Therefore, the annual interest rate is about 46.2\%.

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    Check

    A \;= \;\$250\left(1 + \frac{0.462}{365}\right)^{1095} \:=\:\$998.8298956 \:\approx\:\$999 . . . Yes!

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  4. #4
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    Quote Originally Posted by Soroban View Post
    Therefore, the annual interest rate is about 46.2\%.
    Yes, but the question asks for daily interest rate
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  5. #5
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    Soroban was right. The solutions posted were correct.
    Plus, the question does not ask for the "daily" interest rate. It only asks for the "interest rate", and in reality, all banks state annual interest rates.
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