At the age of 29 , to save for retirement, you decide to deposit $\$ 40$ at the end of each month in an IRA that pays $6 \%$ compounded monthly. a. Use the following formula to determine how much you will have in the IRA when you retire at age 65. \[ \begin{array}{l} A=\frac{P\left[(1+r)^{t}-1\right]}{r} \text { or } \\ A=\frac{P\left[\left(1+\frac{r}{n}\right)^{n t}-1\right]}{\left(\frac{r}{n}\right)} \end{array} \] b. Find the interest. a. You will have approximately $\$ \square$ in the IRA when you retire. (Do not round until the final answer. Then round to the nearest dollar as needed.) b. The interest is approximately $\$ \square$. (Use the answer from part a to find this answer. Round to the nearest dollar as needed.)

Step 1 ：Given that the monthly deposit is $40, the annual interest rate is 6% or 0.06 in decimal form, the interest is compounded monthly so n is 12, and the time is the difference in years between the retirement age and the current age, which is 65 - 29 = 36 years.

Step 2 ：Plug these values into the formula for compound interest: \(A = \frac{P[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}\)

Step 3 ：Calculate the total amount in the IRA: \(A = \frac{40[(1+\frac{0.06}{12})^{12*36}-1]}{\frac{0.06}{12}} = 60997\)

Step 4 ：Calculate the total amount of deposits: \(total\_deposits = 40 * 12 * 36 = 17280\)

Step 5 ：Calculate the total interest earned by subtracting the total amount of deposits from the total amount in the IRA: \(interest = 60997 - 17280 = 43717\)

Step 6 ：Final Answer: a. You will have approximately \(\boxed{60997}\) in the IRA when you retire. b. The interest is approximately \(\boxed{43717}\).