Consider the three stocks in the following table. Pt represents price at time t$,$ and Qt represents shares outstanding at time t$.$

Stock P$0$ Q$0$ P$1$ Q$1$ P$2$ Q$2$

A $85200100200110200$

B $4050060500301000$

C $703008030085300$

Note that Stock B had a $2-$for$-1$ split after the market closed on t$=1.$ P$1=$ $$60$ was stock B$$s price before the split. As a result of the stock split, price fell to $$30$ and shares outstanding increased from $500$ to $1000.$

First, calculate the rate of return on a market value$-$weighted index $($MVWI$)$ of the three stocks for the first period $($t$=0$ to t$=1).$

Second, calculate the price$-$weighted index $($PWI$)$ of the three stocks for t$=0,$ t$=1,$ and t$=2.$