Calculating Inflation-Adjusted Compound Returns
Summary
The document explains how to express compound growth in nominal terms and in terms of purchasing power. It distinguishes a quoted nominal interest rate from a real rate: the nominal rate combines real growth and inflation multiplicatively. To report a future balance in today’s money, the nominally compounded value can instead be deflated by cumulative expected inflation.
For the example, the discussion applies interest of 3% and inflation of 2% over ten years to a principal of $1,000, yielding an inflation-adjusted value of $1,102.48. It also presents an equivalent rate adjustment for that calculation. The exchange highlights an ambiguity: inflation can be treated as part of the nominal return, or as a reduction in future purchasing power. The result depends on which quantity is intended and assumes fixed annual rates; it does not address uncertainty in future inflation or taxes and fees.
Key ideas
- Nominal interest combines real interest and inflation through compounding.
- To express future wealth in today’s purchasing power, deflate its nominal value by cumulative inflation.
- The example compounds the stated interest rate and discounts for the stated inflation rate over the same horizon.
- The meaning of an inflation adjustment depends on whether the goal is nominal growth or real purchasing power.
Tags
Full text
# How do we include inflation in our calculations? # How do we include inflation in our calculations? How do we include inflation in our compound interest calculations? E.g. if we have current principal of `1000$` and the interest rate is 3% after 10 years we have `1344$` (used this calculator) But if for this exercise we wanted to take inflation into account let's say 2% how would that be part of our formula? Update: I know that the number including the inflation is `1102$`. I don't know exactly how to do the calculations to get the `1102$`. Getting the `1334$` is straightforward but I am confused on how to include inflation to get the `1102$` ## Answer by Brumder (score 1) https://quant.stackexchange.com/a/22476 This calculator does not include inflation in whatever interest rate you specify (I checked). Usually, the rate quoted by banks is the nominal interest rate, which is simply how much your capital will appreciate with inflation (e.g. higher inflation would yield higher returns). It does not take into account purchasing power and is calculated as follows: ``` Nominal Rate = (1 + Real Interest Rate)(1 + Inflation Rate) - 1 ``` In terms of trying to "take inflation into account" I'm not totally sure what you mean. If you mean factor inflation into the equation so that the purchasing power of the future value is quoted in today's dollar amount, the simplest way would be to lower the rate you entered into the calculator by expected future inflation (assuming you're using the commonly cited nominal rate or using the interest rate as a proxy for total return). You could also divide the future value from the calculator by: `(1 + expected inflation)^n` ## Answer by Chris Degnen (score 1) https://quant.stackexchange.com/a/22477 Further to a post here, you can appreciate by the interest rate and depreciate by the inflation rate at the same time like this: ``` principal p = 1000 interest rate r = 0.03 inflation i = 0.02 number of years n = 10 p (1 + r)^n (1 + i)^-n = 1102.48 ``` The calculation can be simplified with a factor `x`: ``` x = i (1 + r)/(1 + i) = 0.0201961 p (1 + (r - x))^n = 1102.48 ``` These calculations give the future value in 10 years appreciated by interest at 3% but depreciated by inflation at 2%. However, it differs from the example here, which - like Brumder's initial answer - counts inflation as a appreciating factor.
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