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.