Ana is retiring next year from the school that she has taught at for the last 25 years. Her pension pays a monthly salary of \( \$ 1,562.32 \). She also receives a monthly income from an IRA that she has made regular monthly payments, in the amount of \( \$ 230.32 \), for the last 15 years. If Ana plans on using her pension and the funds from her IRA as her primary source of income for the next 10 years, determine Ana's monthly income given that her IRA compounds interest at \( 2.3 \% \) monthly. Round to the nearest cent. a. \( \$ 2,024.02 \) b. \( \$ 1,887.42 \) c. \( \$ 461.70 \) d. \( \$ 325.10 \)

To determine Ana's total monthly income from her pension and her IRA, we need to calculate the future value of her IRA after 10 years of compounding interest and then add that to her monthly pension income. 1. **Pension Income**: Ana's monthly pension is \( \$ 1,562.32 \). 2. **IRA Income**: Ana has been making regular monthly payments into her IRA for the last 15 years. We need to calculate the future value of her IRA after 10 more years of compounding at a monthly interest rate of \( 2.3\% \). The formula for the future value of a series of cash flows (ordinary annuity) is given by: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( P \) = monthly payment into the IRA = \( \$ 230.32 \) - \( r \) = monthly interest rate = \( 2.3\% = 0.023 \) - \( n \) = total number of payments (10 years × 12 months/year) = \( 120 \) Plugging in the values: \[ FV = 230.32 \times \frac{(1 + 0.023)^{120} - 1}{0.023} \] First, calculate \( (1 + 0.023)^{120} \): \[ (1 + 0.023)^{120} \approx 1.023^{120} \approx 8.052 \] Now, substitute this back into the future value formula: \[ FV = 230.32 \times \frac{8.052 - 1}{0.023} \] \[ FV = 230.32 \times \frac{7.052}{0.023} \approx 230.32 \times 306.174 \approx 70,707.78 \] This is the total future value of the IRA after 10 years. 3. **Monthly Income from IRA**: To find the monthly income from the IRA, we need to divide the future value by the number of months over which she will withdraw the funds (10 years × 12 months/year = 120 months): \[ \text{Monthly Income from IRA} = \frac{70,707.78}{120} \approx 589.23 \] 4. **Total Monthly Income**: Now, we can calculate Ana's total monthly income by adding her pension income and her monthly IRA income: \[ \text{Total Monthly Income} = \text{Pension Income} + \text{Monthly Income from IRA} \] \[ \text{Total Monthly Income} = 1,562.32 + 589.23 \approx 2,151.55 \] However, it seems that the options provided do not match this calculation. Let's check the options again: a. \( \$ 2,024.02 \) b. \( \$ 1,887.42 \) c. \( \$ 461.70 \) d. \( \$ 325.10 \) Since the calculated total monthly income of \( 2,151.55 \) does not match any of the options, it appears there may have been a misunderstanding in the problem or the options provided. If we only consider the monthly income from the IRA without compounding, it would be: \[ \text{Monthly Income from IRA} = 230.32 \] Then the total would be: \[ \text{Total Monthly Income} = 1,562.32 + 230.32 = 1,792.64 \] This still does not match the options. Please verify the problem statement and the options provided.