Problem $4.$ Consider the three stocks in Table $3.P_t$ represents prices at time $t,$ and $Q_t$ represents shares

outstanding at time $t.$ Stock $C$ splits three$-$for$-$one in the last period at $t=2.(25$ points$)$

Table $3$: Stock Index

a$.$ Calculate the rate of return on a equally$-$weighted index of the three stocks for the first period $($from

$t=0$ to $t=1)$

b$.$ Calculate the rate of return on a price$-$weighted index of the three stocks for the second period $($from

$t=1$ to $t=2)$

c$.$ Calculate the rate of return on a market value$-$weighted index of the three stocks for the second period

$($from $t=1$ to $t=2)$