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3 years ago

how much would 600 invested at 8% interest compounded continuously be worth after 3 years? round your answer to the nearest cent

1 answer:

8 0

$\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount}\\\\
A=Pe^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to& \$600\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
t=years\to &3
\end{cases}
\\\\\\
A=600e^{0.08\cdot 3}\implies A=600e^{0.24}$

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Explanation:

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The explicit rule for a geometric sequence can be modeled by:

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Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.

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________________________________

We can test that this works by substituting the number location of the term you want to find.

For instance:

$a_{1} = 32 • (\frac{1}{2})^{1-1}$

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$a_{6} = 32 • (\frac{1}{2})^{6-1}$

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