Eric deposits $4,700 at 1.03% interest, compounded continuously for five years. What's his ending balance?

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.

Find out how to calculate the ending balance of Eric's $4,700 deposit at 1.03% continuously compounded interest over 5 years. Using the continuous compound interest formula, this solution demonstrates how exponential growth affects the final balance. Suitable for high school students in Grades 9-12.

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