Peter accumulated $7,500 in credit card debt. If the interest rate is 3.5% per year and he does not make any payments for 10 years, how much will he owe on this debt in 10 years by compounding continuously? 
Round your answer to the **nearest cent**.
Do **NOT** round until you have calculated the final answer.

To find how much Peter will owe in 10 years with continuous compounding, we can use the formula for continuous compound interest:

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

Where:
- $ A $ is the amount owed after $ t $ years,
- $ P $ is the principal amount (initial debt),
- $ r $ is the annual interest rate (in decimal form),
- $ t $ is the time in years,
- $ e $ is the base of the natural logarithm (approximately 2.71828).

Given:
- $ P = 7,500 $,
- $ r = 3.5\% = 0.035 $,
- $ t = 10 $ years.

Substitute these values into the formula:

\[
A = 7,500 \cdot e^{0.035 \times 10}
\]

Now let's calculate the final amount.After 10 years, with continuous compounding at an interest rate of 3.5%, Peter will owe **$10,643.01**.

Would you like more details on the steps or have any questions?

Here are five related questions to explore:

1. How does the formula change if the interest is compounded annually instead of continuously?
2. What would Peter owe after 5 years instead of 10?
3. How would the amount change if the interest rate was 5% per year?
4. How does continuous compounding differ from other types of compounding (monthly, quarterly, etc.)?
5. How can Peter minimize his debt if he starts making payments before 10 years?

**Tip:** The continuous compounding formula is most effective when interest is applied infinitely often, making it a good approximation for frequent compounding!

Peter accumulated $7,500 in credit card debt. If the interest rate is 3.5% per year and he does not make any payments for 10 years, how much will he owe on this debt in 10 years by compounding continuously? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.

Learn how to calculate continuous compound interest on $7,500 of credit card debt at an interest rate of 3.5% over 10 years. Using the formula A = P * e^(rt), find out how much will be owed after 10 years, rounded to the nearest cent. This problem is suitable for high school students (Grades 9-12) and covers exponential growth in finance.

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