XYZ stock price and dividend history are as follows:

Year Beginning$-$of$-$Year Price Dividend Paid at Year$-$End

$2015$ $ $130$ $ $2$

$20161532$

$20171282$

$20181332$

An investor buys five shares of XYZ at the beginning of $2015,$ buys another two shares at the beginning of $2016,$ sells one share at the beginning of $2017,$ and sells all six remaining shares at the beginning of $2018.$

a$.$ What are the arithmetic and geometric average time$-$weighted rates of return for the investor? $($Do not round intermediate calculations. Round your answers to $2$ decimal places.$)$ b$-1.$ Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January $1,2015,$ to January $1,2018.($Negative amounts should be indicated by a minus sign.$)$ b$-2.$ What is the dollar$-$weighted rate of return? $($Hint: If your calculator cannot calculate internal rate of return, you will have to use a spreadsheet or trial and error.$)($Negative value should be indicated by a minus sign. Round your answer to $4$ decimal places.$)$