you need $50,000 in your bank account in 4 years, how much must be deposited now? The interest rate is 8compounded continuously. Round your answer to the nearest dollar

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

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

Where:
- $A$ is the future value (in this case, $50,000),
- $P$ is the present value or the amount to be deposited,
- $r$ is the interest rate (8% or 0.08),
- $t$ is the time in years (4 years),
- $e$ is Euler's number (approximately 2.71828).

We need to solve for $P$, so rearranging the formula:

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

Now, substituting the known values:

\[
P = \frac{50,000}{e^{0.08 \times 4}}
\]

Let me calculate that for you.To have $50,000 in your bank account in 4 years with an 8% interest rate compounded continuously, you must deposit **$36,307** now.

Do you need any further details or have any questions? Here are 5 related questions to think about:

1. What happens if the interest rate changes to 10%?
2. How does continuous compounding compare with annual compounding in this scenario?
3. What would the deposit need to be if the goal was to have $100,000 in 4 years?
4. How much would you have in 4 years if you deposit $36,307 with 8% interest?
5. What is the formula for compound interest when compounding is done monthly or yearly?

**Tip:** The continuous compounding formula involves Euler's number, $e$, which provides faster growth compared to other compounding intervals.

You need $50,000 in your bank account in 4 years, how much must be deposited now? The interest rate is 8% compounded continuously. Round your answer to the nearest dollar.

Find out how much you need to deposit today to reach $50,000 in 4 years with 8% interest compounded continuously. Using the formula for continuous compounding, this solution demonstrates step-by-step how to calculate the present value. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation