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This problem involves calculating the future value of a series of monthly deposits into an account that compounds interest monthly. The relevant formula for this is the Future Value of an Annuity formula:

\[
FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}
\]

Where:
- $ P $ is the monthly deposit ($75),
- $ r $ is the annual interest rate (2.5%, or 0.025),
- $ n $ is the number of times the interest is compounded per year (12 for monthly compounding),
- $ t $ is the number of years (36 months is 3 years).

Let’s plug in the values:

- $ P = 75 $,
- $ r = 0.025 $,
- $ n = 12 $,
- $ t = 3 $.

Now, I will calculate the future value for you.Matt will have approximately **$2800.80** in 36 months, rounded to the nearest cent.

Would you like more details or have any other questions? Here are some related questions to expand on this:

1. How does compounding frequency affect the future value of investments?
2. What would be the future value if Matt saved for 48 months instead?
3. How would the future value change if the interest rate was 3% instead of 2.5%?
4. What is the difference between simple interest and compound interest in savings accounts?
5. How would the total savings differ if Matt made quarterly instead of monthly deposits?

**Tip:** When saving, frequent deposits and higher compounding frequencies generally result in more interest earned over time.

Matt is saving to buy a new motorcycle. If he deposits $75 at the end of each month in an account that pays an annual interest rate of 2.5%, how much will he have in 36 months? Assume that the compounding is being done monthly.

Learn how to calculate the future value of monthly deposits using the Future Value of Annuity formula. This example involves a $75 monthly deposit, a 2.5% annual interest rate, and 36 months of compounding interest. Suitable for high school and college students.

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