XYZ's stock price and dividend history are as follows:

Year	Beginning-of-Year Price				Dividend Paid at Year-End
2018	$	112			$	4
2019		134				4
2020		101				4
2021		112				4

An investor buys three shares of XYZ at the beginning of 2018, buys another two shares at the beginning of 2019, sells one share at the beginning of 2020, and sells all four remaining shares at the beginning of 2021. 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 answers to 2 decimal places. Do not round other calculations.)

arithmetic average rate of return %

geometric average rate of return %

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, 2018, to January 1, 2021. If your calculator cannot calculate internal rate of return, you will have to use trial and error.) (Round your answer to 4 decimal places. Negative amount should be indicated by a minus sign.)

Dollar-weighted rate of return %