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Math Help - Logarithmic Applications

  1. #1
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    Logarithmic Applications

    I'm doing a compound interest problem and I wanted to know if I am doing it correctly. The problem is


    How long will it take for $1,000 to grow to $5,000 at an interest rate of 3.5% if interest is compounded

    a) quarterly

    b) continuously

    For part a) I used the formula A = P(1 + r/n)^nt

    5,000 = 1,000( 1 + .035/4)^4t

    5 = (1.00875)^4t

    ln5 = 4t ln1.00875

    ln5 / 4ln1.00875 = T

    Did I do it correctly? Perhaps i'm not putting it into the graphing calculator correctly but I keep getting the wrong answer compared to the answer section of the book. If I did do it correctly, can someone let me know what is the correct way to punch that into the calculator? I have a a Ti-83 graphing calculator.

    For part b) I used the continuous forumula of A = Pe^rt

    5,000 = 1,000e^.035t

    5 = e^.035t

    ln5 = .035t

    ln5 / .035 = t

    Did I do that correctly?

    Thanks for any help
    Last edited by JonathanEyoon; July 25th 2007 at 12:13 PM.
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  2. #2
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    Hello, Jonathan!

    How long will it take for $1,000 to grow to $5,000
    at an interest rate of 3.5% if interest is compounded

    a) quarterly

    b) continuously


    For part a) I used the formula: . A \;= \;P\left(1 + \frac{r}{n}\right)^{nt}

    Then: . 5,000 \;= \;1,000\left(1 + \frac{0.035}{4}\right)^{4t}\quad\Rightarrow\quad5 \;= \;(1.00875)^{4t}

    . . \ln5 \:= \:4t\!\cdot\!\ln(1.00875)\quad\Rightarrow\quad t \:=\:\frac{\ln5}{4\!\cdot\!\ln(1.00875)}
    You are probably entering it incorrectly on your calculator.
    Here's one common error . . .


    We want: . (\ln 5) \div \left[4\!\cdot\!\ln(1.0875)\right]

    We must enter: . \boxed{\ln}\;\boxed{5}\;\boxed{)}\;\boxed{\div}\;\  boxed{(}\;\boxed{4}\;\boxed{\times}\;\boxed{\ln}\;  \boxed{1.0875}\;\boxed{)}\;\boxed{=}
    . . . . . . . . . . . . . . . . . {\color{red}\uparrow}
    When we press \boxed{\ln}, the display shows: . \boxed{\ln\,(\qquad}
    . . It automatically supplies the left parenthesis.

    After we have entered the \boxed{5}, we must close the parentheses with \boxed{)}


    If we don't, we will have: . \boxed{\ln}\;\boxed{5}\;\boxed{\div}\;\boxed{4} \cdots
    . . which the calculator interprets as: . \ln\left(\frac{5}{4}\right)

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