Bridget opened a savings account and deposited $800.00 as principal. The account earns 7% interest, compounded continuously. What is the balance after 2 years? Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years. Round your answer to the nearest cent.

To find the balance after 2 years, we can use the formula for continuous compounding:

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

where:
- $ P = 800 $ (the principal),
- $ r = 0.07 $ (the interest rate as a decimal),
- $ t = 2 $ (the time in years),
- $ e \approx 2.71828 $.

### Step-by-Step Solution

1. **Substitute the values** into the formula:
   \[
   A = 800 \times e^{(0.07 \times 2)}
   \]

2. **Calculate the exponent** $ 0.07 \times 2 = 0.14 $, so the equation becomes:
   \[
   A = 800 \times e^{0.14}
   \]

3. **Calculate $ e^{0.14} $**:
   Using the approximate value, $ e^{0.14} \approx 1.15027 $.

4. **Multiply by the principal**:
   \[
   A = 800 \times 1.15027 \approx 920.22
   \]

### Final Answer

The balance after 2 years, rounded to the nearest cent, is **$920.22**.

Would you like more details on continuous compounding, or have any questions?

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1. What would be the balance after 3 years instead of 2?
2. How does continuous compounding compare to annual compounding at the same rate?
3. What if the interest rate were 8% instead of 7%?
4. How would a one-time additional deposit affect the balance in continuous compounding?
5. How does the formula for continuous compounding relate to other compound interest formulas?

**Tip:** Continuous compounding is particularly powerful as it applies the interest constantly, yielding slightly higher results than daily, monthly, or annual compounding at the same rate.

Calculate the balance of a $800 deposit in a savings account with 7% interest, compounded continuously, over 2 years using the formula A = P * e^(rt). Step-by-step solution and explanation for continuous compounding interest. Suitable for high school students in Grades 10-12.

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