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Part 1
Find the compound amount and the amount of interest earned by the following deposit.
​$5200 at 3.8​% compounded continuously for 5 years.


To solve this problem, we use the formula for continuous compounding:

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

where:
- $A$ is the amount of money accumulated after time $t$.
- $P$ is the principal amount (the initial deposit).
- $r$ is the annual interest rate (as a decimal).
- $t$ is the time the money is invested for, in years.
- $e$ is the base of the natural logarithm (approximately 2.71828).

Given:
- $P = 5200$
- $r = 3.8\%$ or $0.038$ as a decimal
- $t = 5$ years

First, calculate the compound amount $A$. Then, the amount of interest earned is simply $A - P$.

Let's calculate these values.The compound amount after 5 years is approximately **$6,288.10**. The amount of interest earned is approximately **$1,088.10**.

Would you like further details, or do you have any other questions?

Here are 5 related questions to explore:
1. What is the difference between continuous compounding and annual compounding?
2. How would the compound amount change if the interest rate were 5% instead of 3.8%?
3. What happens to the interest earned if the principal amount is doubled?
4. How would the time period affect the final amount if it were extended to 10 years?
5. What is the formula for compound interest when interest is compounded semi-annually?

**Tip:** Continuous compounding generally yields a higher return than traditional compounding methods, especially over long periods.

Learn how to calculate the compound amount and interest earned on a $5200 deposit at 3.8% interest continuously compounded over 5 years. Get a detailed solution with step-by-step calculations and understand the impact of continuous compounding on investment returns.

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