How do you calculate annual inflation rate using monthly inflation?

Answer 1

Just a thought based on logic -this is not a textbook answer and all numbers are fictional and in dollars-: If the change in inflation was the same each month you would use a simple compounding formula that is S=P(1+I)^N so to make it simple if you got 100$ (P) today and inflation increases 3.5% each month (I) then in 1 yr (that is 12 months(N)) you would have the following: S= 100$*(1+0.035)^12 à S=151.12$ That is that the 100$ will inflate to 151$ in paper (not in true value) in one year. So 100$ today in 12 months is worth 100/151.12= 66.18% of its original value that is 100$ are worth 33.82% less in this particular example and in dollars of the initial year 66.18$. In 10 yrs (120 months) 100$ with such an inflation rate would be worth 1.6$. For different month by month inflation rates simply do it step by step: i.e. January= 100$+100$*4.2%= 104.2 February=104.2 +104.2* 3.4%=107.742 and goes on for every month. So once you reach the last month of the year simply divide 100/December and the inflation rate will be 100 minus that number. For January and February it is 100/107.742= 92.8 so 100-92.8 gives us 7.2% inflation. Also keep in mind to use crude month to month inflation rates and not year average inflation rates that are the average inflation of each month so far in the year. You will often find rates that are the average of this year's months against the previous year's month average. That is the average of all monthly rates until lets say May of 2009 (Jan+Feb+Marc+April+May/5) against the same of all months until May 2008. If you want to simply see the devaluation of money don't use these rates use monthly rates. Also you can use the inflation rate of this year's month against last year's but calculate it once for each year. For example from Jan 2005 to Jan 2006 = 3.4% and from Jan 2006 to Jan 2007 = 3.6% so the above formula would be Jan 05-06= 100$+100$*0.034=103.4$ Jan 06-07= 103.4$+103.4$*0.036=107.12$. This is 100/107.12= 6.65% inflation. So your 100$ have devalued 6.65% and are worth 100-100*0.0665= 93.35$ today 2 yrs later. Also remember that what is true inflation is not easily calculated and debatable. Take in mind interest rates and other facts i.e. multiplication of money from multiple loaning and the accuracy of reporting from government agencies in third world countries etc.