Find the amount accumulated FV in the given annuity account. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your answer to the nearest cent.) $500 is deposited monthly for 10 years at 3% per year in an account containing $5,000 at the start

To find the amount accumulated in the annuity account, we can use the formula for the future value of an ordinary annuity:

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

Where:
- $FV$ is the future value of the annuity
- $P$ is the monthly deposit
- $r$ is the interest rate per period
- $n$ is the number of periods

In this case, the monthly deposit $P$ is $500$, the interest rate $r$ is $3\%$ per year, and the number of periods $n$ is $10 \times 12 = 120$ months.

First, let's calculate the future value of the $5,000$ initial deposit after $10$ years:

$$FV_{\text{initial deposit}} = 5000 \times (1+ \frac{0.03}{12})^{10 \times 12} \approx 6743.49$$

Next, let's calculate the future value of the monthly deposits:

$$FV_{\text{monthly deposits}} = 500 \times \left( \frac{(1+\frac{0.03}{12})^{10 \times 12} - 1}{\frac{0.03}{12}} \right) \approx 68231.85$$

Finally, we can find the total future value by adding the two amounts:

$$FV = FV_{\text{initial deposit}} + FV_{\text{monthly deposits}} \approx \text{6743.49} + \text{68231.85} = \text{74975.34}$$

Therefore, the amount accumulated in the annuity account is approximately $74,975.34$. Answer: $74975.34.