Mathematics

Question


The amount of money in an account can be determined by the formula A re where is the
initial investment, r is the annual interest rate, and tis the number of years the money was
invested. What is the value of a $5000 investment after 18 years, if it was invested at 4% interest
compounded continuously?

2 Answer

  • Answer: $10272.17

    Step-by-step explanation: Please see attachment for explanation

  • Answer:

    [tex]\$10272.17[/tex]

    Step-by-step explanation:

    Since it is compounded continuously, we will use:

    [tex]A=A_0 \cdot e^{k t}[/tex]

    [tex]A_0[/tex] is the amount invested.

    [tex]k[/tex] is the rate.

    [tex]t[/tex] is the number of years you let the money sit.

    [tex]A[/tex] is the future amount after the [tex]t[/tex] years that has been accumulated.

    (Note:

    I'm going to write [tex]r=4%[/tex] as a decimal. [tex]r=\frac{4}{100}=0.04[/tex].)

    [tex]A=5000 \cdot e^{0.04 \cdot 18}[/tex]

    [tex]A=5000 \cdot e^{0.72}[/tex]

    [tex]A=5000 \cdot 2.0544332[/tex] (approximated)

    [tex]A=10272.16605[/tex] (approximated)

    To the nearest cent this is [tex]\$10272.17[/tex].

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