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Thread: Simple annual investment: express total accumulated amt as fcn of t

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    Simple annual investment: express total accumulated amt as fcn of t

    If a principal of P dollars is invested at a simple annual interest rate of r for t years, express the total accumulated amount of the principal and interest as a function of t. Is your result a linear function of t?

    -Would appreciate immediate help. I'm studying for a university test tomorrow.

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    Elite Member stapel's Avatar
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    Quote Originally Posted by munclesonkey View Post
    If a principal of P dollars is invested at a simple annual interest rate of r for t years, express the total accumulated amount of the principal and interest as a function of t. Is your result a linear function of t?

    -Would appreciate immediate help. I'm studying for a university test tomorrow.
    What is the simple-interest formula? What equation then would represent the ending total amount?

    When you solved this equation for "t=", what did you get?

    Please be complete. Thank you!

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    Quote Originally Posted by stapel View Post
    What is the simple-interest formula? What equation then would represent the ending total amount?

    When you solved this equation for "t=", what did you get?

    Please be complete. Thank you!
    T=I/pr

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    Elite Member mmm4444bot's Avatar
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    A = accumulated amount

    P = principal

    r = decimal form of interest rate

    t = elapsed time (in years)

    The phrase "accumulated amount" means: principal plus interest.

    In other words, if symbol I represents the interest, we have:

    A = P + I

    Now, replace symbol I with the math expression you were given for simple interest.

    A will then be a function of t.

    t and A(t) are the input and output variables, respectively.

    P and r are constants (parameters).
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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    What does "simple interest mean"? NO compounding?
    Example:
    If principal = 1000 and rate = 12%,
    then interest = 1000*.12 =120 annually,
    so worth 1000 + 120*5 = 1600 after 5 years:
    is that correct in your case?
    I'm just an imagination of your figment !

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    Elite Member stapel's Avatar
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    Quote Originally Posted by munclesonkey View Post
    T=I/pr
    So, when you solved the equation "I = Prt" for "t=", you got t = I/(Pr). That's a start. Now let's return to what I asked you before:

    What is the simple-interest formula? What equation then would represent the ending total amount?
    To answer the first equation, your answer is "I = Prt". But what is your answer to the second question? What equation represents the ending total amount? That is, not just the interest on the principle, but the entire ending amount?

    Then, once you have that equation, solve that equation for "t=". What do you get?

    When you reply, please show all your steps. Thank you!

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