# How to adjust for long term inflation in an investment plan

So I have my investment Plan set in March 2019, with initial portfolio value of 250.000€, annual return 11% and long-term inflation rate at 1.5%.

As you can see in column A, I have Capital BoP, Estimated Returns in Column B and Capital EoP in column C.

Column A (except for the first value which is assumed to be 250.000€) is calculated easily as B+C (of previous periods) Column B is calculated as A*(11%-1.5%) Column C is A+B However, I am not sure the formula for adjusting for inflation is correct like that, because we know that the real rate of return is (1+return)/(1+inflation)-1 But I also remember from my studies that this is the formula for the actual inflation, not for the long term inflation, which is fixed from day 1 to infinite.

So my question is simple: how would you calculate the estimated return for each period?

Many thanks

• Why is column A in line 2 not equal to column C in line 1? Isn't the end of the first period the same moment as the start of the next period? It sounds from your description like you're double-counting your earnings, but the numbers don't add up when I look at the table. – The Photon May 9 '19 at 18:55
• For example, how did you make an extra e.860 between the last day of March and the first day of April? That's almost half of the earnings you made in all of March. – The Photon May 9 '19 at 18:57
• I think it’s important to point out that your assumed return and inflation rates are extremely generous for planning purposes. More common rates for planning purposes are 7-10% return and 3-4% for long term inflation. I’m not saying what numbers you should use, but at least look into some of the reasons more conservative rates are usually used to make planning decisions. – T. M. May 9 '19 at 19:16
• It really doesn't matter. Don't worry about the math... Unless you are investing in Madoff 2.0 (or you are trying to be Madoff 2.0) you aren't going to get a sustained 11% long term rate of return. And yes the numbers are WAY off.. Your table shows an annual rate of return that is significantly higher than 11%. – sofa general May 9 '19 at 22:20
• @ThePhoton because there are other columns like dividends (paid on june and december) and savings injection. Sorry for not having explained that. – Saverio May 10 '19 at 9:14

`(1+return)/(1+inflation)-1` would be more accurate (it discounts each year's return by the level of inflation), but your formula is often used as an easy estimate for small levels of inflation:

``````(1.11 / 1.015) - 1 = 9.36%
``````

which is fairly close to the 9.5% you use. To convert to monthly raise it to the 1/12 power:

``````(1.11 / 1.015)^(1/12) - 1 = 0.748%
``````

which is again close to dividing it by 12 (`9.5%/12 = 0.792%`)

Since both the return and inflation are guesses, use whichever formula you prefer (or can explain to someone else if necessary)

• so what about when I convert it to monthly return? assuming that is annual inflation, should I use (1.11/12months)/(1.015/12months)-1? cause, as you can see in the image, i simply calculate, for every cell, (11%-1.5%)/12 – Saverio May 9 '19 at 15:54
• @Saverio See my edit. – D Stanley May 9 '19 at 16:12