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To solve this problem, we need to calculate the future value of a series of monthly deposits made into an account that compounds monthly.

The formula for the future value of a series of equal monthly payments compounded monthly is:

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

Where:
- $FV$ is the future value
- $P$ is the monthly deposit amount ($75)
- $r$ is the monthly interest rate (annual interest rate of 2.5% divided by 12)
- $n$ is the total number of months (36 months)

### Step 1: Convert the annual interest rate to a monthly interest rate.
\[
r = \frac{2.5\%}{12} = \frac{0.025}{12} = 0.00208333
\]

### Step 2: Plug values into the formula.
- $P = 75$
- $r = 0.00208333$
- $n = 36$

\[
FV = 75 \times \frac{(1 + 0.00208333)^{36} - 1}{0.00208333}
\]

### Step 3: Calculate the future value.
First, calculate the exponentiation and subtraction:
\[
(1 + 0.00208333)^{36} - 1 \approx 0.0766851
\]

Now plug this into the formula:
\[
FV = 75 \times \frac{0.0766851}{0.00208333} \approx 75 \times 36.80093 = 2760.07
\]

### Conclusion:
After 36 months, Matt will have approximately **$2,760.07**.

Would you like more details on any part of the calculation or have any questions? 

Here are some additional questions that might interest you:
1. How would the future value change if the interest rate was 3%?
2. What happens if Matt deposits $100 per month instead of $75?
3. How does increasing the number of months from 36 to 48 affect the final amount?
4. How much of the $2,760.07 is from interest earned?
5. What is the total amount Matt contributed in 36 months?

**Tip:** When calculating compound interest, increasing the frequency of compounding periods will lead to slightly higher returns, especially over longer terms.

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 savings deposits with a 2.5% annual interest rate, compounded monthly. Matt deposits $75 each month for 36 months. See how much he will have at the end using the compound interest formula.

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