Formula that describes the value of an initial investment of [tex]\$300[/tex] growing at an interest rate of [tex]6\%[/tex] compounded continuously is equals to [tex]A(t) = 300e^{.06t}[/tex].
What is compounded continuously?
" Compounded continuously is defined as the interest calculation and reinvestment of the amount over infinite period."
Formula used
[tex]A(t) = P e^{rt}[/tex]
[tex]A(t) =[/tex] Final amount
[tex]P =[/tex] Principal amount
[tex]t =[/tex] time period interest is applied
[tex]r=[/tex] rate of interest
According to the question,
Given,
Principal amount [tex]= \$300[/tex]
Rate of interest [tex]= 6\%[/tex]
As per the given condition interest compounded continuously,
Substitute the value in the formula of interest compounded continuously we get,
[tex]A(t) = 300 e^{\frac{6}{100} t}\\\\\implies A(t) = 300 e^{.06 t}[/tex]
Hence, Option (B) is the correct answer.
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