In July 2021, Vio Bank was offering 0.61% interest on its money market account.† Assuming interest is reinvested daily, find the associated exponential model for the value of a $5,000 deposit after t years. Hint: [See this example.]
A(t) =

Assuming that this rate of return continued for 8 years, how much would a deposit of $5,000 in July 2021 be worth in July 2021? (Round your answer to the nearest dollar.)
$

To solve this problem, we need to apply the formula for continuous compound interest. The general formula is:

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

Where:
- $ A(t) $ is the amount of money after $ t $ years.
- $ P $ is the principal (initial deposit).
- $ r $ is the annual interest rate (as a decimal).
- $ t $ is the number of years.
- $ e $ is Euler’s number (approximately 2.71828).

### 1. Finding the exponential model:
- The initial deposit $ P $ is $5,000.
- The annual interest rate is 0.61%, which we convert to decimal form: $ r = 0.0061 $.
- Interest is compounded continuously, so we use the continuous compounding formula.

Thus, the exponential model for the value of the deposit after $ t $ years is:

\[
A(t) = 5000 \cdot e^{0.0061t}
\]

### 2. Finding the value after 8 years:
To find the value of the $5,000 deposit after 8 years, substitute $ t = 8 $ into the exponential model:

\[
A(8) = 5000 \cdot e^{0.0061 \times 8}
\]

Let me calculate that for you.After 8 years, a deposit of $5,000 in July 2021, with a 0.61% interest rate compounded continuously, would be worth approximately **$5,250**.

Would you like more details or have any questions? 

Here are five related questions to expand on this:
1. What is the formula for compound interest if the compounding is done monthly instead of continuously?
2. How would the result change if the interest rate were compounded annually instead of daily?
3. How does continuous compounding differ from discrete compounding in terms of return over time?
4. What would be the value of the deposit if the interest rate were 1.5% instead of 0.61%?
5. How long would it take for the $5,000 deposit to grow to $6,000 at the same interest rate?

**Tip:** Continuous compounding provides the highest possible return compared to any other compounding frequency for the same interest rate.

In July 2021, Vio Bank was offering 0.61% interest on its money market account. Assuming interest is reinvested daily, find the associated exponential model for the value of a $5,000 deposit after t years. Assuming that this rate of return continued for 8 years, how much would a deposit of $5,000 in July 2021 be worth in July 2021? (Round your answer to the nearest dollar.)

Learn how to calculate the exponential growth of a $5,000 deposit with a 0.61% interest rate compounded continuously. Using the continuous compound interest formula A(t) = P * e^(rt), find the value of the deposit after 8 years. This problem is suitable for high school students in 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