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Math Help - Growth and Compound Iterest formulas

  1. #1
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    Growth and Compound Iterest formulas

    Hi,

    I've just read the section on Exponential Growth and Decay functions. Then I was doing exercises from that section and to solve my problems I often used this function

    y = Ce^(kt)

    which is an Exponential Growth and Decay function.
    Then I was trying to solve a problem about Compound interest (from the same section) and again I was trying to use the same function above. But when I looked to check my answers, I was surprised as they used another function to solve the problem:

    Amount = P(1 + r/n)^nt where t in years, r is rate at which the amount is compounded, and n is the proportionality constant (1, 12, or 365) I believe

    So, my question is how these two formulas are different? Why they used another formula to find a compound interest, and why y = Ce^(kt) cannot be used instead?

    Thanks
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by Pupka View Post
    Hi,

    I've just read the section on Exponential Growth and Decay functions. Then I was doing exercises from that section and to solve my problems I often used this function

    y = Ce^(kt)

    which is an Exponential Growth and Decay function.
    Then I was trying to solve a problem about Compound interest (from the same section) and again I was trying to use the same function above. But when I looked to check my answers, I was surprised as they used another function to solve the problem:

    Amount = P(1 + r/n)^nt where t in years, r is rate at which the amount is compounded, and n is the proportionality constant (1, 12, or 365) I believe

    So, my question is how these two formulas are different? Why they used another formula to find a compound interest, and why y = Ce^(kt) cannot be used instead?

    Thanks
    This isn't a calculus question. But anyways:

    A = P(1 + r/n)^(nt) is refered to as the compounding interest function where compounding occurs at intervals (like once every month).
    y = Ce^(kt) is the infinitly compounding function, where compounding occurs constantly, such as in the growth of bacteria.

    Think of it this way, after a certain amount of time if you leave money in a bank they will add more money to your account (usually about .3% for me ) on top of what you already had, but if they used the exponential growth function they would constantly be adding money into your account rather than once every month or so.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Pupka View Post
    Hi,

    I've just read the section on Exponential Growth and Decay functions. Then I was doing exercises from that section and to solve my problems I often used this function

    y = Ce^(kt)

    which is an Exponential Growth and Decay function.
    Then I was trying to solve a problem about Compound interest (from the same section) and again I was trying to use the same function above. But when I looked to check my answers, I was surprised as they used another function to solve the problem:

    Amount = P(1 + r/n)^nt where t in years, r is rate at which the amount is compounded, and n is the proportionality constant (1, 12, or 365) I believe

    So, my question is how these two formulas are different? Why they used another formula to find a compound interest, and why y = Ce^(kt) cannot be used instead?

    Thanks
    ecMathGeek is absolutely correct. You should look at the way the question is phrased to know which formula to use.

    if the question has the phrase: "compounded continuously" or "compounded exponentially" or "continously compounded" use the formula:

    y = Ce^(kt)

    if the question has the phrase: "compounded monthly (or yearly or daily or whatever time interval)" use the formula:

    Amount = P(1 + r/n)^nt
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ecMathGeek View Post
    usually about .3% for me
    You should thank your lucky stars! I get 0.25%

    we should both open an Orange Savings account, i think they give 4 maybe 5% interest!
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  5. #5
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    Quote Originally Posted by ecMathGeek View Post
    This isn't a calculus question. But anyways:
    Exponential Growth and Decay function was first introduced to me in Calc IIand there they had a compound interest questions as well.



    Quote Originally Posted by ecMathGeek View Post
    A = P(1 + r/n)^(nt) is refered to as the compounding interest function where compounding occurs at intervals (like once every month).
    y = Ce^(kt) is the infinitly compounding function, where compounding occurs constantly, such as in the growth of bacteria.

    Think of it this way, after a certain amount of time if you leave money in a bank they will add more money to your account (usually about .3% for me ) on top of what you already had, but if they used the exponential growth function they would constantly be adding money into your account rather than once every month or so.
    Thanks for explanation. Was very helpful and understanding
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Pupka View Post
    Exponential Growth and Decay function was first introduced to me in Calc IIand there they had a compound interest questions as well.
    well you are partially right. exponential growth and decay is in calculus, but it should not be where you got introduced to it. the first time you see it should be in pre-calculus, and maybe college algebra depending on your school. but after that, it shows up everywhere! calc 1 and 2, differential equations, chemistry, physics, business math, and the list goes on and on
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  7. #7
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    Quote Originally Posted by Jhevon View Post
    well you are partially right. exponential growth and decay is in calculus, but it should not be where you got introduced to it. the first time you see it should be in pre-calculus, and maybe college algebra depending on your school. but after that, it shows up everywhere! calc 1 and 2, differential equations, chemistry, physics, business math, and the list goes on and on
    Yeah, I believe you mean this A = Pe^(rt) which is the same thing. Yeah, this formula and compound interest I remember from algebra, but there they only used it in Interest problems rather than applying it to a bunch of other things (such as bacteria or population growth) where the initial conditions are also involved. In calc this function is proved and its applications are more advanced as to compare with algebra.
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