To calculate the ending balance of Eric's deposit with continuously compounded interest, we use the formula for continuous compounding:

$A = P e^{rt}$

Where:

• $A$ is the ending balance (the amount of money after interest).
• $P$ is the initial principal (Eric's initial deposit), which is $4,700.
• $r$ is the annual interest rate (1.03%, or 0.0103 in decimal form).
• $t$ is the time the money is invested (5 years).
• $e$ is Euler's number (approximately 2.71828).

Now, substituting the known values:

$A = 4700 \times e^{0.0103 \times 5}$

Let's calculate the value of $A$.After 5 years, Eric's ending balance with continuously compounded interest is approximately $4,948.39.

Would you like further details or explanations?

Here are five related questions to expand on this concept:

1. What if the interest rate were compounded annually instead of continuously?
2. How would the balance change if the interest rate increased to 2%?
3. What would happen if Eric invested the same amount for 10 years instead of 5 years?
4. How does continuous compounding compare to monthly compounding in terms of balance growth?
5. How would inflation affect the real value of Eric's ending balance?

Tip: Continuous compounding generally results in a slightly higher ending balance than other compounding methods, but the difference grows with time.