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Relation between nominal and real returns and inflation

Relation between nominal and real returns and inflation. Created by Sal Khan.

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  • purple pi purple style avatar for user Alex
    At the end of the video, Sal says that (1+N)=(1+R)(1+I) makes a ton of sense.
    Why is that, from a basic theoretical standpoint?
    (31 votes)
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    • mr pants teal style avatar for user Wrath Of Academy
      I think the equation is more logical when you have Real rate is Nominal divided by Inflation. Ie, your Real rate is how much your Nominal rate is beating Inflation by.

      The way he wrote it, Real rate times Inflation rate equals the Nominal rate you would need. Which makes sense, too, but sounds weirder to me.
      (2 votes)
  • leaf grey style avatar for user Rtm.
    at - where did the first 1+I (the denominator) goes? He cancels the numerator, but where does the denominator go?
    (12 votes)
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  • blobby green style avatar for user LordRussell
    is this the Fisher Effect?
    (5 votes)
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    • spunky sam blue style avatar for user Daniel White
      An economic theory proposed by economist Irving Fisher that describes the relationship between inflation and both real and nominal interest rates. The Fisher effect states that the real interest rate equals the nominal interest rate minus the expected inflation rate. Therefore, real interest rates fall as inflation increases, unless nominal rates increase at the same rate as inflation. in other words: The Fisher effect can be seen each time you go to the bank; the interest rate an investor has on a savings account is really the nominal interest rate. For example, if the nominal interest rate on a savings account is 4% and the expected rate of inflation is 3%, then money in the savings account is really growing at 1%. The smaller the real interest rate the longer it will take for savings deposits to grow substantially when observed from a purchasing power perspective.
      (16 votes)
  • blobby green style avatar for user safi
    I still dont get why Sal is simplifying at the end in green color? any simple explanation? thank you!
    (3 votes)
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    • aqualine ultimate style avatar for user Abdulaziz.Saja
      You twist and turn an equation however you like as long as you stick to the correct mathematical principals. The last move was just to make everything that much clearer from a logical viewpoint. He's saying the nominal rate of growth (1+N) equals the real rate of growth (1+R) times the inflation rate (1+I).
      (6 votes)
  • blobby green style avatar for user menasir22
    How did he get rid of P? Theres only one P for each? At
    (2 votes)
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    • blobby green style avatar for user mikybee93
      Imagine it like this, in a simpler fashion:

      (p*a - p*b)/ p*c

      Both of the values on top are divided by the single value on the bottom, so the single P on the bottom can get rid of both Ps on the top.

      Does that answer the question?
      (5 votes)
  • blobby green style avatar for user Pierre Bonnici
    why is 1 = (1+I) / (1+I) ??
    (1 vote)
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  • leafers seed style avatar for user John Yale
    I can see how "( ( 1 + N ) - ( 1 + I ) ) / ( 1 + I ) = Real Rate" is a useful formula given that the principal (P), the nominal rate (N), and the inflation rate (I) are pre-determined and a financial advisor or economist would be tasked to find the real rate of return for a client or an employer, etc.

    How is the end game of this video, resulting in "( 1 + N ) = ( 1 + R ) ( 1 + I )", an applicable equation in a real life scenario? For example would it be useful for the same financial advisor or economist to cross-check or provide proof of their work? Just curious, thanks!
    (2 votes)
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  • aqualine ultimate style avatar for user Jenny P
    throughout the video, Sal says "compounded by nominal/real interest rate". what does that mean?
    (1 vote)
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    • orange juice squid orange style avatar for user Owen Sechrist
      compound is a tricky word that has a nuanced meaning. The most useful definition here would be something along the lines of "to make bigger or greater by counting all the parts of the whole"
      So you are taking the the original amount and ending up with a new amount (the new "whole") that counted the original amount and the effect of the interest rate (the "parts" of the "whole").
      Therefore you a compounding the original to arrive at the new.

      If that still is not clear, here is a physical analogy: A compound bow is a bow that uses a pulley system to compound the amount effort spent drawing the bowstring.
      (2 votes)
  • male robot johnny style avatar for user perry.rippetoe
    Does anyone know how to calculate CPI?
    (1 vote)
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  • leaf green style avatar for user Ahmed Al-Attar
    What if the inflation rate equals the market interest rate, then if we find the real interest rate
    i'=(i-f)/(1+f)=0
    You are paying a series of five constant-dollar (or real-dollar) uniform payments of $2411.66 beginning at the end of first year. Assume that the general inflation rate is 29.79% and the market interest rate is 29.79% during this inflationary period.

    The equivalent present worth of the project is:
    (0 votes)
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Video transcript

Let's generalize the mathematics that we've been doing in the last few videos to calculate the real return. And maybe we'll come up with some interesting formulas or some simple approximations. So what we've been doing is we've been, at least in the first video, we converted everything to today's dollars. So the actual dollar return in today's dollars is the amount that we got or the net dollar return. And the net dollar return is the amount that we originally invested compounded by the nominal interest rate. And here we're assuming that we're writing it as a decimal. So in the example we've been using it was 10%. And so this is going to be 0.10. Or this whole value is going to be 1.10. And so this is how much we're going to get after a year has passed. So in our example, this was the $110. $100 compounded by 1.1. And then from that, you want to subtract how much we invested in today's dollars. Well, we originally invested P dollars a year ago. And in today's dollars, we just need to grow it by the rate of inflation. And in the examples we've been doing we assume that the rate of inflation is 2%. So that would be 0.02. So this expression right over here is actually the dollar return in today's dollars. It's this value right here that we calculated in the first video. And to calculate the real return we want the dollar return in today's dollars divided by the investment in today's dollars. And once again, this is the investment in today's dollars. It's the amount we invested originally grown by inflation. And this right over here gives us the real return. Now one thing we can do right off the bat to simplify this is that we have everything in the numerator and everything in the denominator is divisible by P. So let's divide the numerator and the denominator by P. Simplify it a little bit. Just like that. And then we get in the numerator, we get 1 plus N minus 1 plus I. I'll write it like that still. All of that over 1 plus I is equal to R. And I'm giving some space here because one simplification I can do here is I can add 1 to both sides of this equation. So if I add a 1 on the right hand side, I have to add a 1 on the left hand side. But a 1 is the same thing as a 1 plus I over a 1 plus I. This is completely identical because this is dividing the same thing by itself. So this is going to be a 1. So we're adding a 1 on the left. We're adding a 1 on the right. And the reason why I did that is it comes up with an interesting simplification. We have the same denominator here. If I add the numerators, 1 plus I plus 1 plus N minus 1 plus I. So this and this are going to cancel out. And we're going to be left with, in the numerator, we're just left with a 1 plus the nominal interest rate. In the denominator, we just have a 1 plus the rate of inflation is equal to 1 plus the real interest rate. And then we can multiply both sides times the 1 plus I. Multiply both sides times 1 plus I. And we get interesting result. And to some degree, this is a common sense result. And I want to show you that it's completely consistent with everything we've been doing so far. These guys cancel out. And when you compounded by the nominal interest rate, that's the same thing as growing the real growth, and then that compounded by the rate of inflation, which actually makes a ton of sense.