XYZ's stock price and dividend history are as follows: Year Beginning-of-Year Price Dividend Paid at Year-End 2017 $ 150 $ 4 2018 180 4 2019 130 4 2020 150 4 An investor buys three shares of XYZ at the beginning of 2017, buys another two shares at the beginning of 2018, sells one share at the beginning of 2019, and sells all four remaining shares at the beginning of 2020.

a. What are the arithmetic and geometric average time-weighted rates of return for the investor? (Round your year-by-year rates of return and final answer to 2 decimal places. Do not round other calculations.)

b. What is the dollar-weighted rate of return? (Hint: Carefully prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1, 2017, to January 1, 2020. If your calculator cannot calculate IRR, you will have to use trial and error or a spreadsheet program.) (Round your answers to 4 decimal places. Negative amount should be indicated by a minus sign.)