# Value of money (incomes) question - what is the “r” here?

I would like some help with a fairly basic "value of money" question. (I'm very much a beginner in this field so please bear with me.)

I'm writing about income changes throughout a decade (2010-2019). And I would like to convert a bunch of random incomes (lump sums) from different years to their "2020" value.

I found the formula for the present and future value calculations. My problem is that I do not know what to put in place of the "r" and if I'm using the right formula.

Suppose that I have an amount of $3000, and this amount is an income in the year 2011. Now do I understand it correctly that I need to use the FV formula if I want to know its value for the current year (2020)? So it would look something like: FV = 3000 x (1+r1) x (1+r2) ... x (1+r9), right? (9 because 2020-2011 = 9, that's why I wrote 9, correct me if I'm wrong please) Similarly, with another example, would$5000 from 2019 look like this for 2020: FV = 5000 x (1+r1) ? So just one r.

But what exactly is r? Is it simply the inflation for each year? Do I just take the yearly inflation rate of my country in each year from 2011 to 2019 and use it as r1, r2, r3 etc.? Or from 2012 to 2020? IF it really is just the inflation rate, then for r1 do I start with the inflation rate of 2011 or 2012? If I'd like to see the value of a 2011 lump sum for 2020, then r1 should be the inflation rate of 2012? Or what do I put in the place of r if not this?

OR do I have to do something entirely different to get the results I need?

Thanks in advance, any help is very much appreciated!!

This question implies to me that you want to convert historical incomes to “2020 dollars”. The standard way to do that is to use the consumer price index (CPI). Note that this is the level, not the rate of change (“inflation rate”).

The formula for a year T is straightforward:

(Income in “2020 dollars”) = (income in year T) *(CPI index in 2020)/(CPI in year T).

For example, if the income was \$100 in a year where the CPI was 60, and the 2020 CPI is 110, the income in 2020 dollars is \$100*(110/60).

If you wanted to convert future incomes to 2020 dollars, you would need to create an assumed inflation rate. You would either use the PV formula, or use the above formula with an extrapolated CPI. How the future inflation rate is determined is your decision.

• Okay, so would it then be incorrect to use the FV formula with the inflation rates for each year in the formula? In what way would that result and the one you suggested be different? Thanks – Vermilion Apr 30 at 16:15
• Are you discussing historical data? In which case you just use the index level. It’s only future values that you requires you to use an assumed inflation rate. – Brian Romanchuk Apr 30 at 18:53
• Yes the incomes are all in the past decade. The inflation is not assumed as the years are in the past and I can find the rates, no? I have several different incomes during different years and I was told that 100 dollars now cannot be directly compared to 100 dollars ten years ago. So now I'm trying to bring all the past incomes to a comparable common ground in 2020. What you first describe seems just what I need, but could I also do this with the FV formula, applied for a 2011 income with the inflation rates of 2011, 2012 ... 2020 as the r value? As in what's the FV of a 2011 income for 2020? – Vermilion Apr 30 at 20:10
• You need the CPI index levels. It would take more work to use the inflation rates - you would need to do the equivalent of calculating the index levels. – Brian Romanchuk Apr 30 at 21:35
• Alright, but do I need the CPIs to refer to a common year? Because for the country I'm looking at, I found the CPI levels to always use the previous year as "100". Wouldn't I need one fixed year in the past as 100 for the others to be correct in my graph? So e.g. CPI in 2012 takes CPI in 2011 as "100", whereas CPI in 2013 takes CPI in 2012 as "100". Is this a problem? – Vermilion May 1 at 8:23