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.