Annabelle invested $70,000 in an account paying an interest rate of 6.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, *to the nearest ten dollars*, would be in the account after 9 years?

To find the amount of money in the account after 9 years, we use the continuous compounding formula:

\[
A = P \cdot e^{rt}
\]

Where:
- $ A $ is the amount after 9 years.
- $ P = 70{,}000 $ dollars (the principal).
- $ r = 6.1\% = 0.061 $ (the interest rate as a decimal).
- $ t = 9 $ years.

Substituting the values into the formula:

\[
A = 70{,}000 \cdot e^{0.061 \cdot 9}
\]

\[
A = 70{,}000 \cdot e^{0.549}
\]

Now, calculate $ e^{0.549} $:

\[
e^{0.549} \approx 1.731
\]

Then:

\[
A \approx 70{,}000 \cdot 1.731 \approx 121{,}170
\]

To the nearest ten dollars, the amount in the account after 9 years is approximately **$121,170**.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How much interest did Annabelle earn after 9 years?
2. How would the amount change if the interest rate were 5.5% instead of 6.1%?
3. What would be the amount after 15 years with the same interest rate?
4. How does the final amount compare if the compounding is annual instead of continuous?
5. How long would it take for Annabelle's investment to double with the same interest rate?

**Tip:** When dealing with continuous compounding, small changes in the interest rate or time can have a significant impact on the final amount, so it's important to be precise in calculations.

Learn how to calculate compound interest with continuous compounding using the formula A = P * e^(rt). This problem involves calculating the amount of money in an account after 9 years with a principal of $70,000 and an interest rate of 6.1% compounded continuously.

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