Question content area top Part 1 Use the savings plan formula to answer the following question. You put ​$200 per month in an investment plan that pays an APR of 4.5​%. How much money will you have after 28 ​years? Compare this amount to the total deposits made over the time period. Question content area bottom Part 1 After 28 years the investment plan will contain ​$    enter your response here. ​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

To solve this, you can use the future value of a series formula (also known as the future value of an annuity formula): \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is the future value of the investment, - \( P \) is the monthly deposit ($200), - \( r \) is the monthly interest rate (APR/12 = 0.045/12), - \( n \) is the total number of deposits (28 years × 12 months). First, calculate the monthly interest rate: \[ r = \frac{0.045}{12} \approx 0.00375 \] Now, calculate \( n \): \[ n = 28 \times 12 = 336 \] Now plug those values into the formula: \[ FV = 200 \times \frac{(1 + 0.00375)^{336} - 1}{0.00375} \] Calculating this: 1. \( (1 + 0.00375)^{336} \approx 3.9352 \) (approximately), 2. \( (3.9352 - 1) \approx 2.9352 \), 3. \( FV \approx 200 \times \frac{2.9352}{0.00375} \approx 200 \times 782.72 \approx 156544 \). Finally, round to the nearest cent: **After 28 years, the investment plan will contain approximately $156,544.00.** Now, compare to total deposits made: Total deposits made over 28 years: \[ 200 \times 336 = \$67,200 \] So, after 28 years, you will have about **$156,544.00**, compared to total deposits of **$67,200**. That's a significant gain thanks to the power of compounding interest!