To complete this, we'll use the formula for continuous compounding, since it's compounded continuously. The formula is:

$A = Pe^{rt}$

where:

• $P = 5000$ (principal),
• $r = 0.02$ (interest rate as a decimal),
• $t = 20$ (time in years),
• $e \approx 2.71828$ (base of the natural logarithm).

Step-by-Step Calculation

1. Substitute the values into the formula: $A = 5000 \cdot e^{(0.02 \times 20)}$

2. Calculate the exponent: $0.02 \times 20 = 0.4$

3. Now, find $e^{0.4}$: $e^{0.4} \approx 1.4918$

4. Multiply by the principal: $A = 5000 \cdot 1.4918 \approx 7459.00$

So, the balance $A$ after 20 years is approximately $7459.00.

Would you like further details on any steps?

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Further Related Questions

1. How does continuous compounding differ from other compounding frequencies?
2. What would the balance be if compounded annually instead?
3. How would the balance change with a different interest rate?
4. What if the investment duration was shorter, such as 10 years?
5. How does compounding impact the total balance over long-term investments?

Tip

Continuous compounding yields slightly higher returns than periodic compounding due to constant reinvestment of interest.