Khloe invested $160 in an account paying an interest rate of 5.7% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest ten dollars, would be in the account after 17 years?

To calculate the amount of money in the account after 17 years with continuous compounding, we use the formula for continuous compound interest:

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

Where:
- $A$ is the amount of money in the account after $t$ years,
- $P$ is the principal amount (initial investment),
- $r$ is the annual interest rate (expressed as a decimal),
- $t$ is the time in years,
- $e$ is Euler's number (approximately 2.71828).

Given:
- $P = 160$ (initial investment),
- $r = 5.7\% = 0.057$,
- $t = 17$ years.

We can now calculate $A$:

\[
A = 160 \times e^{0.057 \times 17}
\]

Let me calculate this for you.After 17 years, Khloe would have approximately $420 in the account, rounded to the nearest ten dollars.

Would you like more details on how this was calculated, or do you have any other questions?

Here are five related questions to expand on this topic:
1. How would the amount change if the interest rate were 6% instead of 5.7%?
2. What is the difference between continuous compounding and annual compounding?
3. How much would Khloe have after 10 years instead of 17 years?
4. How does continuous compounding compare to quarterly compounding at the same rate?
5. What happens to the investment if the principal is doubled?

**Tip:** Continuous compounding maximizes growth as it constantly applies interest to the balance, making it more powerful than other compounding methods.

Learn how to calculate continuous compound interest for an investment of $160 at a rate of 5.7% over 17 years. Using the exponential growth formula A = P * e^(rt), this example demonstrates how interest accumulates over time. Suitable for students in Grades 10-12.

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