How much money needs to be deposited now into an account to obtain $6,700 in 15 years if the interest rate is 7% per year compounded continuously?

$
.

The formula to calculate the present value for continuous compounding is:

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

Where:
- $ P $ is the present value (the amount you need to deposit now),
- $ A $ is the future value (in this case, $6,700),
- $ r $ is the interest rate (7% or 0.07),
- $ t $ is the time in years (15 years),
- $ e $ is Euler's number (approximately 2.71828).

Now let's calculate:

\[
P = \frac{6700}{e^{0.07 \times 15}}
\]

Let me calculate that for you.The amount that needs to be deposited now is approximately **$2,344.58** to obtain $6,700 in 15 years at a 7% interest rate compounded continuously.

Do you want more details or have any questions?

Here are 5 related questions for further exploration:
1. How does continuous compounding compare to annual compounding in terms of returns?
2. What would the required deposit be if the interest rate were 5% instead of 7%?
3. How would the deposit change if the time period were 20 years instead of 15 years?
4. What is the formula for compounding with different intervals (e.g., monthly or quarterly)?
5. How can I calculate future value if I make regular monthly contributions instead of a lump sum?

**Tip:** Continuous compounding yields the highest possible interest compared to other compounding frequencies (annual, quarterly, etc.) because interest is constantly being added.

How much money needs to be deposited now into an account to obtain $6,700 in 15 years if the interest rate is 7% per year compounded continuously?

Learn how to calculate the present value required to obtain $6,700 in 15 years with a 7% interest rate, compounded continuously. This problem involves exponential growth concepts, the continuous compounding formula, and Euler's number. Suitable for students in Grades 10-12.

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