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 $2,000 deposit after t years. Hint: [See this example.]
A(t) =  2000(1+
0.0061
365​)365t   
Correct: Your answer is correct.
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Assuming that this rate of return continued for 7 years, how much would a deposit of $2,000 in July 2021 be worth in July 2020? (Round your answer to the nearest dollar.)
$   

To calculate the value of a $2,000 deposit with a 0.61% annual interest rate, compounded daily, we will use the formula for compound interest:

\[
A(t) = P \left(1 + \frac{r}{n}\right)^{nt}
\]

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),
- $ n $ is the number of times interest is compounded per year,
- $ t $ is the number of years.

Given:
- $ P = 2000 $,
- $ r = 0.0061 $ (since 0.61% = 0.0061),
- $ n = 365 $ (compounded daily),
- $ t = 7 $ years.

Let’s substitute these values into the formula and compute the value.

\[
A(7) = 2000 \left(1 + \frac{0.0061}{365}\right)^{365 \times 7}
\]

Now, I will calculate this.After 7 years, a $2,000 deposit at an annual interest rate of 0.61%, compounded daily, would be worth approximately **$2,087** in July 2028.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand on this concept:
1. How would the value change if interest were compounded monthly instead of daily?
2. What would the final amount be if the interest rate was 1% instead of 0.61%?
3. How does daily compounding compare to annual compounding in terms of final value over 7 years?
4. How long would it take for the $2,000 to grow to $2,500 at the same interest rate?
5. How does inflation affect the real value of money in accounts like this?

**Tip**: Even small differences in interest rates or compounding frequency can significantly affect the final value over time!

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 $2,000 deposit after t years. Assuming that this rate of return continued for 7 years, how much would a deposit of $2,000 in July 2021 be worth in July 2028?

Learn how to calculate the future value of a $2,000 deposit in a Vio Bank money market account at 0.61% interest, compounded daily over 7 years. Understand the formula for compound interest and its application to real-world finance problems. Suitable for students in Grades 11-12.

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