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### Course: Macroeconomics > Unit 4

Lesson 2: Nominal v. real interest rates- Real and nominal return
- Calculating real return in last year dollars
- Nominal interest, real interest, and inflation calculations
- Relation between nominal and real returns and inflation
- Indexing and its limitations
- Lesson summary: nominal vs. real interest rates
- Nominal vs. real interest rates

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# Nominal interest, real interest, and inflation calculations

While the nominal interest rate is the agreed upon percentage that someone will pay back on a loan, the real interest rate accounts for inflation and gives a more accurate representation of the actual value of the loan over time.

## Want to join the conversation?

- Hi, @3:02min in the video, we arrive at the number 1.0294. Could you please explain the calculation that led you to arrive at the value of 2.94% (the real interest rate)? The video does not explain that step. Thanks!(2 votes)
- We calculate a 5% interest rate as 1.05 (the original amount + 5%) we can infer that the same goes for the 1.0294 which is the original amount + 2.94%. In other words, subtract by 1 Then multiply by 100 to get the real interest rate.(2 votes)

- Why do we divide the nominal interest rate by the rate of inflation? what does it mean by the rate of inflation being multiplied by cost?(1 vote)
- Recall that inflation is a increase in the price level of goods (such as the CPI). Therefore, the rate of inflation multiplied by the cost is the purchasing power of the initial investment when you get the money back, in this case, after one year. Instead of calculating the real return, we are calculating the real interest rate which is the real return +1. For example:

100×1.05/100×1.02. The 100's cancel each other out and we are left with 1.05/1.02=1.0294. The real return is (105-102)/102=0.0294. In other words, finding real return and real interest rate are more or less the same thing. The real interest rate is a multiplier and the real return is how much the purchasing power of the original investment has increased.(1 vote)

- How to know inflation rate from GDP deflator(1 vote)
- The GDP deflator is (nominal GDP/real GDP) x 100, and it tells you how much inflation is. For example, if nominal GDP is $105 and real GDP is $100, then inflation is 5%.(1 vote)

- How to know the calculations of nominal interest, real interest and inflation?(1 vote)

## Video transcript

- [Instructor] Let's say that you agree to lend me some money. Say, you agree to lend me $100. And I ask you, all right, do I just have to pay you back $100? And you say, no, no,
you want some interest. And I say, how much interest? And you say that you
are going to charge me 5% per year interest. So one way to think
about it is if I borrow $100 today, so $100 today, in a year I'm going to
have to pay you back $100 times, I'm gonna
have to grow it by 5%, so that's the same thing
as multiplying it by 1.05. This is how much I'm
going to have to pay back. Let me write this down. This is borrow. This is what I'm going
to have to pay back. And so this interest rate,
that just the face value of how much more I'm
gonna have to pay back, this is known as the
nominal interest rate. Nominal interest rate. And we can compare this
to the real interest rate. And you might say, why do we need some other type of interest rate? Well, even though on the face value I'm paying you back 5% more, that doesn't necessarily mean that you're going to be able to buy 5% more with the money
that you get paid back. And you might guess why that is the case. Because of inflation. $105 will not necessarily
buy you in a year what it might buy you today. And so that's what the real interest rate is trying to get at. And to do that, to calculate
our real interest rate, we are going to have to
think about inflation. So let me put inflation right over here. And so let's say that we are in a world that has 2% inflation. So an indicative, a basket of
goods that cost $100 today, if this is the inflation rate, would cost $102 in a year. So there's two ways folks will calculate the real interest rate, given the nominal interest
rate and the inflation rate. The first way is an approximation, but it's very simple and
you can do it in your head. And that's why it's often the
first way that it's taught, but it's not exactly
mathematically correct. So the first way you'd say, well, this could approximately be equal to the nominal interest rate
minus the inflation rate. So you could say this could
be approximately equal to 5% minus, minus 2%, which would be equal to 3%. And this is a decent approximation. But the actual way that you
would want to calculate this if you wanted to be more
mathematically precise is that your nominal interest rate multiplies things by 1.05, so 1.05. But then things are getting more expensive at a rate of 2% per year. Or another way to think about it, costs are being multiplied
by 1.02 every year. So we divide by that
amount, 1.2 every year. And so this was going to give us 1.05 divided by 1.02 is equal to 1.0294. 1.0294. And another way to think about it, we just got a much better sense of what the real interest rate is. It's actually much closer, 2.94% interest. And this is a very small difference, and so that's why people like this method. You can do it in your head
and it got pretty close. But keep in mind, even very small changes in interest can make a big deal when we compound over many years. And in other videos we've
talked about compounding.