a) Explain how dollar cost averaging affects your returns when drawing down your portfolio, for example, by withdrawing a fixed dollar amount from a stock market indexed fund in retirement. Give an example. Explain how dollar cost averaging affects your returns when accumulating assets, as in saving a regular dollar amount and investing in a stock market indexed fund before retirement. Give an example. If the rate of return on U.S. small cap stocks averages 12.5%, and inflation averages 2.5%, how long will it take for you to double the amount of an investment? (Show all work.)

b) Starting with nothing, how much would you need to save and invest at the beginning of each weak in a U.S. equity mutual fund (say based on the S&P 500, that averages 10% per year and has a standard deviation of 20% per year over long periods of time), to have a portfolio worth $1,000,000 in 20 years? State all assumptions and show your work.