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

Year	Beginning-of-Year Price				Dividend Paid at Year-End
2017	$	180			$	4
2018		200				4
2019		170				4
2020		180				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.)

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, 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.)

Dollar-weighted rate of return

%