How much will you need to save per month to have $200,000 after 12 years if your account earns 5% interest per year, compounded monthly?

(a) Explain the concept of compound interest and how it applies to savings over time.
(b) Outline the variables and parameters involved in the question, such as the interest rate, time period, and target savings amount.
(c) Describe the formula or method used to calculate the monthly savings needed, considering the compounding frequency.
(d) Discuss any considerations or assumptions made in the calculation, and the significance of rounding the answer to the nearest cent.