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## Macroeconomics

### Course: Macroeconomics>Unit 4

Lesson 2: Nominal v. real interest rates

# Relation between nominal and real returns and inflation

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

## Want to join the conversation?

• 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?
• 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.
• at - where did the first 1+I (the denominator) goes? He cancels the numerator, but where does the denominator go?
• Ah! Just get it:
(1+I) / (1+I) + [(1+N) - (1+I)] / (1+I) is the same as: [(1+I) + (1+N) - (1+I)] / (1+I)
meaning the dominator does not change, simple rule: 1/2 + 2/2 = 3/2
• is this the Fisher Effect?
• 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.
• I still dont get why Sal is simplifying at the end in green color? any simple explanation? thank you!
• 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).
• How did he get rid of P? Theres only one P for each? At
• 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.

• why is 1 = (1+I) / (1+I) ??
(1 vote)
• Algebra. anything divided by itself is 1
(except 0/0)
• 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!
• throughout the video, Sal says "compounded by nominal/real interest rate". what does that mean?
(1 vote)
• 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.