2. (10 pts) For ten years, you deposit $\$ 700$ every month in an account paying $5.4 \%$ annual interest compounded monthly. Afterward, you leave your money in the same account (still paying 5.4\% annual interest compounded monthly) for 30 more years.
(a) How much money is in the account at the end of the 40 years?

Step 1 ：Given that you deposit $700 every month for 10 years in an account paying 5.4% annual interest compounded monthly, we first calculate the total amount in the account after these 10 years. This can be calculated using the formula for the future value of a series of payments (or annuities): \(FV = P \times \left(\left(1 + \frac{r}{n}\right)^{n \times t} - 1\right) \div \frac{r}{n}\), where \(P\) is the monthly deposit, \(r\) is the annual interest rate, \(n\) is the number of times that interest is compounded per year, and \(t\) is the number of years.

Step 2 ：Substituting the given values into the formula, we get \(FV = 700 \times \left(\left(1 + \frac{0.054}{12}\right)^{12 \times 10} - 1\right) \div \frac{0.054}{12}\).

Step 3 ：After 10 years, you leave your money in the same account for 30 more years. The total amount in the account after these 30 years can be calculated using the formula for compound interest: \(A = FV \times \left(1 + \frac{r}{n}\right)^{n \times t}\), where \(FV\) is the future value calculated earlier, \(r\) is the annual interest rate, \(n\) is the number of times that interest is compounded per year, and \(t\) is the number of years.

Step 4 ：Substituting the given values into the formula, we get \(A = FV \times \left(1 + \frac{0.054}{12}\right)^{12 \times 30}\).

Step 5 ：Calculating the above expressions, we find that the total amount in the account at the end of the 40 years is approximately $559,138.74.

Step 6 ：\(\boxed{559138.74}\)