$(10$ points$)$ Stock market index

MSCI has a Global Bank index including three stocks as follows: Sperbank, Nordea, and Citi. Their stock prices $($Pt$)$ and total shares outstanding $($Qt$)$ from day $0$ to day $2$ are shown as follows:

$\backslash$table$[[,$P$0,$Q$0,$P$1,$Q$1,$P$2,$Q$2],[$Sperbank$,20,100,15,100,10,100],[$Nordea$,20,200,15,200,25,200],[$Citi$,80,200,55,400,30,800]]$

Citi pays two mega stock dividends in day $1$ and day $2,$ resulting in a doubling of the total shares outstanding in both days.

a$.$ If the Global Bank Index is a price$-$weighted index, calculate the rates of return in day $0$ to $t=1)$ and day to $t=2).$

b$.$ If the Global Bank Index is an equally$-$weighted index, calculate the rates of return for day $1$ and day $2.$

c$.$ If the Global Bank Index is a market$-$value$-$weighted index, calculate the rates of return for day $1$ and day $2.$