The four stocks below will be used to answer the questions that follow. You are advised to review Lesson $8$: Securities and Markets, Note $3$: Stock Splitting.

$\backslash$table$[[$Name of company,# of shares,Price @ time t$,$Price @ time t$+1],[$Michelangelo$,200,10,13],[$Leonardo$,1,15,10],[$Raphael$,100,20,22],[$Donatello$,50,25,23]]$

a$.$ Compute a price$-$weighted index by adding the stocks' prices at time $t$ and time $t+1.$ What is the percentage change in the index?

b$.$ Compute a value$-$weighted index by adding the market values of the stocks at time $t$ and time $t+1$ What is the percentage change in the index?

c$.$ Why is there a difference between your answers to parts a and b$?$