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Math Help - Bank Compounding

  1. #1
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    Bank Compounding

    I can't seem to get these problems solved. I have attempted to follow examples given, but I continue to get stuck at a certain point in the process. Please can someone help? Thanks kindly.

    Bank Account

    If a bank compounds continuous, then the formula becomes simpler, that is A=P e^(rt) where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the hundredth's place.

    Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). Round your answer to the hundredth's place.

    A commonly asked question is, "How long will it take to double my money?" At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
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    Last edited by CaptainBlack; January 27th 2007 at 10:14 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by fw_mathis View Post
    I can't seem to get these problems solved. I have attempted to follow examples given, but I continue to get stuck at a certain point in the process. Please can someone help? Thanks kindly.

    Bank Account

    If a bank compounds continuous, then the formula becomes simpler, that is A=P e^(rt) where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the hundredth's place.

    Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t). Round your answer to the hundredth's place.

    A commonly asked question is, "How long will it take to double my money?" At 8% interest rate and continuous compounding, what is the answer? Round your answer to the hundredth's place.
    By the look of this you have missed some data out.

    RonL
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  3. #3
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    Hello, fw_mathis!

    You left out most of the problem . . .


    If a bank compounds continuously, the formula becomes simpler.
    That is: . A \:=\:Pe^{rt} where e is a constant,
    . . r is the annual interest rate and t is the number of years.

    Calculate A with continuous compounding.
    Round your answer to the hundredth's place.

    I assume this is the last half of your previous post.
    Then: . P = 20,\!000,\;r = 0.08,\;t = 3 . . . right?

    We have: . A \;=\;20,\!000e^{(0.08)(3)}\;\approx\;\boxed{\$25,\  !424.98}



    Now suppose, instead of knowing t, we know that the bank
    return to us $25,000 with the bank compounding continuously.
    Using logarithms, find how long we left the money in the bank (find t).
    Round your answer to the hundredth's place.

    The equation becomes: . 25,\!000 \:=\:20,\!000e^{0.8t}\quad\Rightarrow\quad e^{0.08t}\:=\:1.25

    Take logs: . \ln\left(e^{0.08t}\right) \:=\:\ln(1.25)\quad\Rightarrow\quad 0.08t\ln(e) \:=\:\ln(1.25)

    Therefore: . 0.08t\:=\:\ln(1.25)\quad\Rightarrow\quad t \:=\:\frac{\ln(1.25)}{0.08}\:\approx\:\boxed{2.79\  text{ years}}



    A commonly asked question is, "How long will it take to double my money?"
    At 8% interest rate and continuous compounding, what is the answer?
    Round your answer to the hundredth's place.

    We want our \$20,\!000 to grow to \$40,\!000.

    The equation is: . 40,\!000 \:=\:20,\!000e^{0.08t}\quad\Rightarrow\quad e^{0.08t} \:=\:2

    Take logs: . \ln\left(e^{0.08t}\right) \:=\:\ln 2\quad\Rightarrow\quad 0.08t\ln(e)\:=\:\ln 2

    Therefore: . 0.08t\:=\:\ln 2\quad\Rightarrow\quad t\:=\:\frac{\ln 2}{0.08}\:\approx\:8.66\text{ years}

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