Problem $4$ Consider the three stocks in the following table. $P_t$ represents price at time $t,$ and $Q_t$

represents shares outstanding at time t$.$ Stock C splits two for one in the last period.

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

to $t=1.$

b$.$ What must happen to the divisor for the price$-$weighted index in year $2?$

c$.$ Calculate the rate of return for the second period to $t=2.$