This problem involves calculating the future value of an investment with monthly deposits and compounded interest. Anton makes a $1,250 deposit at the start and continues depositing $1,250 every month for 2 years. The interest rate is 2.325% annually, compounded monthly.

To calculate the future value, we break the calculation into two parts:

1. The future value of the initial $1,250 deposit.
2. The future value of the monthly deposits of $1,250 for 24 months.

Step 1: Future Value of the Initial Deposit

The formula for future value with compound interest is:

$FV = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $P$ is the principal amount (initial deposit) = 1250
• $r$ is the annual interest rate = 0.02325
• $n$ is the number of times interest is compounded per year = 12 (monthly)
• $t$ is the time in years = 2

Substituting into the formula:

$FV_{\text{initial}} = 1250 \left(1 + \frac{0.02325}{12}\right)^{12 \times 2}$

Step 2: Future Value of the Monthly Deposits

The formula for the future value of a series of regular deposits (an annuity) is:

$FV_{\text{annuity}} = P \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$

Where:

• $P$ is the monthly deposit amount = 1250
• $r$ is the annual interest rate = 0.02325
• $n$ is the number of times interest is compounded per year = 12
• $t$ is the time in years = 2

Substituting into the formula:

$FV_{\text{annuity}} = 1250 \times \frac{\left(1 + \frac{0.02325}{12}\right)^{12 \times 2} - 1}{\frac{0.02325}{12}}$

Now let's calculate both parts and sum them up to get the total future value.The total amount Anton will have in the account at the end of the two-year period is approximately $31,987.47.

Would you like more details or have any further questions on this calculation?

Here are five related questions to consider:

1. What would happen if the interest were compounded quarterly instead of monthly?
2. How would the final amount change if Anton deposited $1,500 each month instead of $1,250?
3. What if the interest rate was increased to 3%? How much would the account hold in two years?
4. How much of the total amount is from the initial and monthly deposits versus the interest earned?
5. What if Anton wanted to save for 3 years instead of 2? How would the final balance change?

Tip: For long-term investments, small changes in the interest rate or compounding frequency can significantly impact the total future value.