
How much interest is earned on an account that has a rate of 3.67% compounded continuously for 22 years with a initial balance of $445,000?



The formula to calculate continuously compounded interest is:

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

Where:
- $A$ is the final amount (including interest),
- $P$ is the initial principal (in this case, $445,000),
- $r$ is the annual interest rate (3.67% or 0.0367),
- $t$ is the time in years (22 years),
- $e$ is the mathematical constant (approximately 2.71828).

We are looking for the interest earned, so we will first calculate $A$, then subtract the initial principal $P$ from it to find the interest.

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

Let's calculate this.The interest earned on the account after 22 years, with a continuously compounded rate of 3.67%, is approximately **$552,721.60**.

Do you want further details or have any questions? 

Here are 5 related questions to consider:
1. How does continuously compounded interest differ from other compounding methods?
2. What would happen if the interest rate increased to 5%?
3. How does the interest earned change if the time is reduced to 10 years?
4. Can this method be applied to any type of investment or only savings accounts?
5. How does the final amount compare if the interest is compounded annually instead of continuously?

**Tip:** Continuously compounded interest maximizes the growth compared to other compounding frequencies (like annually or quarterly), as it assumes the interest is constantly being calculated and added.

How much interest is earned on an account that has a rate of 3.67% compounded continuously for 22 years with an initial balance of $445,000?

Learn how to calculate interest on an account with a 3.67% continuously compounded rate over 22 years. Using the formula A = P * e^(rt), this problem demonstrates how exponential growth applies to interest calculations. Suitable for Grades 10-12 students studying exponential functions and interest rates.

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