If $\$ 4000$ is deposited into an account paying a nominal interest rate of $7 \%$ per year, how much is in the account 5 years later if interest is compounded (round all answers to the nearest cent; do not write your answers with commas): (a) annually? \$ (b) continuously? \$

Step 1 ：Given that the principal amount (P) is $4000, the annual interest rate (r) is 7% or 0.07, and the time (t) is 5 years.

Step 2 ：For part (a), we use the formula for compound interest which is \(A = P(1 + \frac{r}{n})^{nt}\), where A is the amount of money accumulated after n years, including interest, n is the number of times that interest is compounded per year. In this case, n = 1 (since interest is compounded annually).

Step 3 ：Substituting the given values into the formula, we get \(A = 4000(1 + \frac{0.07}{1})^{1*5}\)

Step 4 ：Solving the above expression, we get \(A = 5610.21\)

Step 5 ：For part (b), we use the formula for continuous compounding which is \(A = Pe^{rt}\), where A is the amount of money accumulated after n years, including interest, e is the base of the natural logarithm, approximately equal to 2.71828.

Step 6 ：Substituting the given values into the formula, we get \(A = 4000e^{0.07*5}\)

Step 7 ：Solving the above expression, we get \(A = 5676.27\)

Step 8 ：Final Answer: (a) The amount in the account 5 years later if interest is compounded annually is \(\boxed{5610.21}\). (b) The amount in the account 5 years later if interest is compounded continuously is \(\boxed{5676.27}\).