$1.(80$ points$)$ Consider the four stocks in the following table with information provided on their prices and the number of outstanding shares where Price $\backslash (\_\{$t$\}\backslash )$ and Shares $\backslash (\_\{$t$\}\backslash )$ denote the price and the outstanding shares at time $\backslash ($ t $\backslash )$ respectively. $($a$)$ What is the rate of return on a price$-$weighted index index of these stocks over the period $2023$ to $\backslash (2024?\backslash )($b$)$ What is the rate of return on a value$-$weighted index index of these stocks over the period $2023$ to $2024?($c$)$ What is the rate of return on an equal$-$weighted index index of these stocks over the period $2023$ to $2024?($d$)$ Now suppose that stock A does a $1-$for$-4$ reverse stock split in $2024.$ What must be the new divisor on the price$-$weighted index in $\backslash (2024?\backslash )$