1: Calculating inflation (20 points) In this question, you will use monthly CPI data to calculate the inflation rate both as a year-on-year growth rate in the price level and as an annualized growth rate. The following table shows data for the CPI and the core CPI from January 2021-October 2022 Date: 2021-01-01 CP 262.200 Core CP 270.114 2021-02-01 263.346 270.522 2021-03-01 265.028 271347 2021-04-01 266.727 273.669 2021-05-01 268.599 275,715 2021-06-01 270.955 277.922 2021-07-01 272.184 278.794 2021-08-01 273.092 279.306 2021-09-01 274214 280017 2021-10-01 276.590 281.705 2021-11-01 278524 2021-12-01 280126 283.179 284.770 2022-01-01 281.933 286,431 2022-02-01 284,182 287.878 2022-03-01 287,708 288.811 2022-04-01 288.663 290.455 2022-05-01 291474 292.289 2022-06-01 295.328 294.354 2022-07-01 295.271 295.275 2022-08-01 295 620 296950 2022-09-01 296.761 298660 2022-10-01 298 062 299 471 a. Use this data to calculate the year-on-year inflation rates for September 2022 and October 2022 using both the overall CPI and core CPI. Make sure to show your work (not only the final answer) b. Explain your answer to (a) 11 Is the year-on-year measure a forward-looking or backward-looking measure of inflation? What happened to overall inflation between September 2022 and October 2022? What is the difference between the definition of the CPI and the definition of core CPI? Use this definition to interpret the difference between overall and core inflation in October 2022. c. Now calculate annualized inflation rates for September 2022 and October 2022. Show your work. Remember that you don't need to memorize the formula; you can find it in the class slides on Blackboard. d. Explain your answer to (c): 11. Is the annualized measure a forward-looking or backward-looking measure of inflation? Compare the year-on-year measure of inflation in October 2022 to the annualized measure. Which is bigger? What does this comparison suggest about whether inflation is speeding up or slowing down