On her 25th birthday, a young woman engineer decides to start saving toward building up a retirement fund that pays 6% interest compounded monthly the market interest rate). She feels that $1,000,000 worth of purchasing power in today's dollars will be adequate to see her through her sunset years after her 65th birthday. Assume a general inflation rate of 4% per year. 

(a) If she plans to save by making 480 equal monthly deposits, what should be the amount of her monthly deposit in actual dollars? Assume the first deposit is made at the end of first month. The amount of monthly deposit in actual dollars is $ 2411. 

(b) If she plans to save by making end-of-the-year deposits, increasing by $1,000 over each subsequent year, how much would her first deposit be in actual dollars? The amount of the first deposit in actual dollars is S.