To calculate the amount of money in Annabelle's account after 9 years with continuous compounding, we can use the formula for continuous compound interest:

$A = P \times e^{rt}$

Where:

• $A$ is the amount of money in the account after $t$ years.
• $P$ is the initial principal (the initial amount invested), which is $70,000.
• $r$ is the annual interest rate, expressed as a decimal, so 6.1% becomes 0.061.
• $t$ is the number of years the money is invested, which is 9 years.
• $e$ is the base of the natural logarithm (approximately 2.71828).

Now, plugging the values into the formula:

$A = 70,000 \times e^{0.061 \times 9}$

First, calculate $0.061 \times 9$:

$0.061 \times 9 = 0.549$

Now, calculate $e^{0.549}$:

$e^{0.549} \approx 1.732$

Then, multiply by the principal:

$A \approx 70,000 \times 1.732 = 121,240$

To the nearest ten dollars, the amount in the account after 9 years will be approximately $121,240.

Let me know if you need further details or have any questions!

Here are 5 related questions to explore:

1. How would the total amount change if the interest rate were 5% instead of 6.1%?
2. How much interest would Annabelle earn in 9 years from the $70,000 investment?
3. What would the amount be if the interest were compounded annually instead of continuously?
4. How would the result change if the investment was for 5 years instead of 9?
5. If Annabelle started with $50,000 instead of $70,000, how much would be in the account after 9 years at the same interest rate?

Tip: When dealing with continuous compounding, using the formula $A = P \times e^{rt}$ gives a quick and accurate calculation, but you must always ensure that the interest rate is in decimal form (e.g., 6.1% = 0.061).