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## AP®︎/College Macroeconomics

### Course: AP®︎/College Macroeconomics > Unit 4

Lesson 2: Nominal vs. real interest rates# Real and nominal return

The real interest rate reflects the additional purchasing power gained and is based on the nominal interest rate and the rate of inflation. Learn how to find the real interest rate in this video. Created by Sal Khan.

## Want to join the conversation?

- I think we can talk about real interest rate (discounting inflation) and nominal interest rate. With that assumption, i thought that the real interest rate were simply calculated by substrating the inflation value to the nominal interest rate.

How come that with the example given in the video the result is 7,8% and not 8% (real interest rate = nominal interest rate - inflation rate => 8 = 10 - 2)?(42 votes)- Great question - I thought Sal might do simple rate subtraction. However, this division method he uses is more realistic. Consider a really extreme example where your investment rate is 200% (so you triple your money after a year) and inflation is 100% (so you'd need to double your money after a year just to stay even). So now you have $100 - in a year you get $300. Inflation means you need $200 in a year just to stay even. So the division method is (300-200)/200 or 50%. That should make sense because $300 is really 50% better than $200 - that's how far you run in front of inflation in a year. The subtraction method would be 200% - 100% = 100%, and that's clearly not right - you didn't out-pace inflation by 100%. (To beat inflation by 100%, you would need $400 in a year - double the inflation-adjusted value of $200.)(58 votes)

- what is the meaning of diversification?(17 votes)
- diversification = spreading out the risk, think of the phrase never put all your eggs in one basket (If the basket is dropped, all is lost.) diversification is putting your eggs in a bunch of different baskets(62 votes)

- Why does govt changes interest rates when inflation changes?(0 votes)
- when a central bank changes the interest rates, and the retail banks follow, it affects the amount of spare money in people's pockets.

A clear example is a mortgage.

When the central bank increases rates, athe the reatil banks follow suit, my mortgage payments go up (I have a flexible rate mortgage). Mortgage rates go uop for folks wanting to remortgage.

Because I have less money left at the end of the month, my consumption of other goods and services drops.

Because the consumption of good and services drops, a downwards pressure is exerted on prices, which causes inflation to drop (or be less high than otherwise).

The opposite is also true.

When central bank rates drop, folks can get cheap credit, and are likely to increase their consumption of goods and services, which in turn means that an upwards pressure is exerted on prices, causing them to rise (and thus price inflation), or to fall more slowly than otherwise (heading off a recession/deflation, like has happened in many countries post 2007/8, and even longer in Japan).(4 votes)

- Wouldn't it be more practical to measure the output of an economy in goods produced/sold and not in money value?(1 vote)
- And that also doesn't take into account non-good services, and considering a significant portion of most economies is the service sector, that's not the most practical option.(6 votes)

- what is nominal money and real money? Can you give some examples of real money?(2 votes)
- Nominal money is the actual amount of money you have at a given moment without taking into account inflation. People use Real Money to take into account the change in price level.(6 votes)

- How did he get 102 from 2% .(1 vote)
- $100 times 2% is $2. That added to the original $100 is $102.(5 votes)

- This was very helpful. However, I have a small doubt. This was for a cashflow of 1 year. Say we have a $100 investment which we held for 5 years. It's given us a CAGR of 10%. Say the average inflation rate during those 5 years is 5%. How would I calculate my real rate of return then ?(1 vote)
- go back to Sal's videos on infaltion.

Remember when he uses (1+r)^n.(2 votes)

- lnflation measures change in

(A) Absolute prices

(B) Relative prices

(C) Both absolute and relative prices

(D) All of the above(0 votes)- A - absolute prices. Inflation is basically looking at "how much does this cost now?" and "how much did this cost back in X year?" and doing the math to see the variance.(4 votes)

- so the nominal return equals return money / previous year and real return equals to return money / today. is it right?(0 votes)
- Nope.

Nominal return = (Interest Earned in today's money)/(Principal Invested in the previous year)

Real Return = (Interest Earned in today's money)/(Principal Invested in today's money)(1 vote)

- Why would he say 8/102=7.8%(0 votes)

## Video transcript

Let's say last year I put $100
into some type savings account in a bank. So this is a year ago. And that now today, exactly
one year later, that $100 has grown to $110. So this is now. So if you look at things just
in the absolute dollar terms, things have grown by $10. So I made $10 off of an
original $100 investment. So I got a 10% return. But what I want to think
about is does this really capture how much more I
can buy with this $110 than I could buy with
that $100 before. Can I really by 10% more
goods and services today than I could a year ago? And to think about
that, let's think about a hypothetical
inflation rate from last year to this year. So let's say that the
inflation ended up being 2% between a
year ago and today. If that's the case, what is $100
a year ago in today's money? Well, if inflation was
2%, then $100 a year ago would buy you the same stuff
that $102 would buy you today. So it would be $102. So what is the dollar
return in today's money, the current purchasing power? Well, we're getting $110. And we invested in
today's money $102. If we look at it
from today's terms, we invested something that
gives us the same purchasing power as $102 today. And now it's giving us a
purchasing power of $110. So we've gotten $8 more
of purchasing power in today's money. So what is the
actual real return? And we can do it
in today's money. And you could do it either way. You could discount the 110
back to a year ago money and figure out the real
return there, and figure out the product actual dollar
return, and do the calculation. Or you can do it
in today's money. And maybe I'll do it the
previous way in the next video. But the real return is we made
$8 over the course of the year in today's money. And what we originally invested
in today's money was $102. And so we get our
calculator out. 8 divided by 102 is 7.8%. So this is equal to 7.8%. So even though the
nominal return, if we just look at what we got in
exchange for what we invested, even though the
nominal return was 10%, because there was 2% inflation
our actual purchasing power only increased by 7.8%.