Find the compound amount and the amount of interest earned by the following deposit.
​$5900 at 3.3​% compounded continuously for 6 years.

To solve for the **compound amount** and the **interest earned** with continuous compounding, we use the formula for continuous compounding:

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

Where:
- $ A $ is the final amount (compound amount),
- $ P $ is the principal amount (initial deposit),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ t $ is the time in years,
- $ e $ is the base of the natural logarithm (approximately 2.71828).

### Given:
- $ P = 5900 $ (initial deposit),
- $ r = 3.3\% = 0.033 $ (interest rate),
- $ t = 6 $ years.

Now we calculate the compound amount $ A $:

\[
A = 5900 \times e^{0.033 \times 6}
\]

\[
A = 5900 \times e^{0.198}
\]

Using $ e^{0.198} \approx 1.219 $:

\[
A \approx 5900 \times 1.219 = 7192.1
\]

So, the **compound amount** is approximately $ A = 7192.10 $.

### To find the interest earned:
\[
\text{Interest} = A - P = 7192.10 - 5900 = 1292.10
\]

Thus, the **interest earned** is approximately $1292.10.

Would you like further details on the steps or calculations?

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Here are 5 related questions for practice:
1. What is the compound amount for $4500 at 5% compounded continuously for 4 years?
2. How would the interest change if the rate were 4.5% instead of 3.3%?
3. What is the formula for compound interest with annual compounding?
4. Can you derive the general formula for compound interest from first principles?
5. What is the difference between continuous and periodic compounding in terms of growth?

**Tip:** Continuous compounding grows slightly faster than periodic compounding because interest is added constantly.

$5900 at 3.3​% compounded continuously for 6 years. Find the compound amount and the amount of interest earned.

Learn how to calculate the compound amount and interest for a deposit of $5900 at a 3.3% interest rate compounded continuously over 6 years. This problem uses the continuous compounding formula A = P * e^(rt) and explores exponential growth in financial math. Suitable for high school students in Grades 10-12.

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