I need the math behind these answer

(1) (20 points) A benchmark index has three stocks X, Y, and Z. The stock prices and shares outstanding at t=0 and t=1 are as follows. t0 t=1 Number of Shares Number of Shares Stock Price Stock Price Outstanding Outstanding Stock X 120 $76 120 $72 Stock Y 150 $126 $70 Stock Z 200 $56 | 200 $60 300 (1) What is the new divisor for a price-weighted index? (Answer: 2.2674) (2) Calculate the rate of return on a price-weighted index of the three stocks for the period (t = 0 to t= 1). (Answer: 3.59%) (3) If the index is a market value-weighted index and the market value-weighted index was 218 at t=0, what is the new index value at t=1? (Answer: 231.45) (4) If the index is an equal weighted index and the equal-weighted index was 218 at t=0, what is the new index value at t=1? (Answer: 227.44)