You deposit $2000 at 3.25% annual interest compounded continuously. How much do  you have after 2 years?

To calculate the amount of money in an account after 2 years with continuous compounding, we can use the formula for continuous compound interest:

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

Where:
- $ A $ is the amount after time $ t $,
- $ P $ is the initial principal (deposit),
- $ r $ is the annual interest rate (in decimal),
- $ t $ is the time in years,
- $ e $ is the mathematical constant approximately equal to 2.71828.

Given:
- $ P = 2000 $ (the initial deposit),
- $ r = 3.25\% = 0.0325 $,
- $ t = 2 $ years.

Now, let's plug the values into the formula and calculate $ A $:

\[
A = 2000 \cdot e^{0.0325 \cdot 2}
\]

I will calculate the result for you.After 2 years, with continuous compounding at an annual interest rate of 3.25%, your deposit of $2000 would grow to approximately **$2134.32**.

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

Here are 5 related questions you might find interesting:
1. How would the final amount change if the interest rate was 5% instead?
2. What if the interest was compounded quarterly instead of continuously?
3. How long would it take for the amount to double at 3.25% interest compounded continuously?
4. How would the final amount differ with a higher initial deposit of $5000?
5. What would happen if you deposited the money for 5 years instead of 2?

**Tip:** Continuous compounding grows your money at the fastest rate possible for a given interest rate!

You deposit $2000 at 3.25% annual interest compounded continuously. How much do you have after 2 years?

Calculate the final amount of a $2000 deposit after 2 years with continuous compounding at an annual interest rate of 3.25%. This problem demonstrates exponential growth using the formula A = P * e^(rt), suitable for Grades 10-12.

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