Mathematics

Question

The formula to determine continuously compounded interest is A = Pe^rt, where A is the amount of
money in the account, P is the initial investment, r is the interest rate, and t is the time, in years.
What equation could be used to determine the value of an account with an $18,000 initial
investment at an interest rate of 1.25% for 24 months?

1 Answer

  • Answer:

    [tex]A=18000 \cdot e^{0.0125 \cdot 2}[/tex]

    [tex]A=18455.67[/tex] (Approximated)

    Step-by-step explanation:

    [tex]A=Pe^{rt}[/tex]

    We are given the following along with the equation we are to use:

    [tex]P=18000[/tex]

    [tex]r=1.25\%=\frac{1.25}{100}=0.0125[/tex]

    Be careful it says [tex]t[/tex] is in years and it gives us a time that is in months.

    [tex]12 \text{months}=1 \text{ year}[/tex]:

    [tex]t=\frac{24}{12}=2[/tex]

    Let's plug in our information:

    [tex]A=18000 \cdot e^{0.0125 \cdot 2}[/tex]

    Plugging in the right hand side into my calculator gives:

    [tex]A=18455.67[/tex] (Approximated)

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