Compounded Continuously

Discussion in 'Other Pre-University Math' started by nycmathguy, Oct 11, 2021.

  1. nycmathguy

    nycmathguy

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    Section 3.1
    54 & 56

    20211011_104108.jpg

    I need the formula needed to do this. Thanks.
     
    nycmathguy, Oct 11, 2021
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  2. nycmathguy

    MathLover1

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    The continuous compounding formula says A = Pe^(rt ) where 'r' is the rate of interest.
    For example, if the rate of interest is given to be 10% then we take r = 10/100 = 0.1.

    Example : Jim invested $5000 in a bank that pays an annual interest rate of 9% compounded continuously. What is the amount he can get after 15 years from the bank? Round your answer to the nearest integer.

    Solution:

    To find: The amount after 15 years.

    The initial amount is P = $5000.

    The interest rate is, r = 9% = 9/100 = 0.09.

    Time is, t = 15 years.

    Substitute these values in the continuous compounding formula,

    A = Pe^(rt)

    A = 5000 * e^(0.09*15)) ≈ 19287

    The answer is calculated using the calculator and is rounded to the nearest integer.

    Answer: The amount after 15 years = $19,287.
     
    MathLover1, Oct 11, 2021
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  3. nycmathguy

    nycmathguy

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    I will use your sample questions to answer 54 & 56.
     
    nycmathguy, Oct 11, 2021
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  4. nycmathguy

    nycmathguy

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    Question 54

    I will do 54 for t = 10 only.

    A = Pe^(rt)

    A = (12,000)e^(0.06)(10)

    A = $21,865.4256

    A = $21,865.43

    Question 56

    I will do 56 for t = 20 only.

    A = Pe^(rt)

    A = (12,000)e^(0.035)(20)

    A = $24,165.03249

    A = $24,165.03
     
    nycmathguy, Oct 12, 2021
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  5. nycmathguy

    MathLover1

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    correct
     
    MathLover1, Oct 12, 2021
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  6. nycmathguy

    nycmathguy

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    You see, one course at a time works best for me.
     
    nycmathguy, Oct 12, 2021
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