Wing Sze is saving for her retirement. She puts her money in an account paying 4.5% interest compounded annually.

a) After 30 years she has exactly $1,000,000. How much money did she start out with? (To the nearest $0.01)

b) If instead of annual compounding, her account paid 4.5% compounded monthly, how many months sooner would she have reached her goal of (at least) $1,000,000?