Part 1

Finding the polynomial according to the given points

Using Newton Interpolating polynomial.

Home Part 2
Newton Interpolating Polynomial

S&P 500®'s Defined Data.

source: Investing.com

Date Closed       X      
Point
Y
(Closing Value)
Aug 1, 2021 1 4,522.68
Sep 1, 2021 2 4,307.54
Oct 1, 2021 3 4,605.38
Nov 1, 2021 4 4,567.00
Dec 1, 2021 5 4,766.18
Jan 1, 2022 6 4,515.55
Feb 1, 2022 7 4,373.79
Mar 1, 2022 8 4,530.41
Apr 1, 2022 9 4,131.93
May 1, 2022 10 4,132.15
Jun 1, 2022 11 3,785.38
Jul 1, 2022 12 4,130.29
Aug 1, 2022 13 3,955.00
Sep 1, 2022 14 3,585.62
Oct 1, 2022 15 3,871.98
Nov 1, 2022 16 4,080.11
Dec 1, 2022 17 3,839.50
Jan 1, 2023 18 4,076.60
Feb 1, 2023 19 3,970.15
March 1, 2023 20 4,109.31


Output: