Alright. Now, let's see how the inflation rate affects the interest rate on loans or savings. Let's see that relationship. Okay. So we've talked about inflation a bit and remember that inflation, we're just talking about the increase in prices over time. Right? So maybe last year something cost $100, and this year, it costs $102. That change in the price, that's the inflation. So, so far we've been using the CPI. Remember, that's the consumer price index to calculate inflation. So, the consumer price index takes the value of goods in different years, and then it sees how those values have changed. So we're calculating inflation with this formula here where we take the CPI in the current year minus the CPI in the previous year divided by the CPI in the previous year times 100 to make a percentage. Now, this is just a percentage change formula, right? We're just seeing the percentage change in prices. And when we talk about percentage change, we're just taking the new number minus the old number divided by the old number, and that's exactly what we did here. Right? The new being the current year, the old being the previous year, new minus old divided by old.
So let's see the relationship that inflation has with interest rates. So when we go to the bank, and we deposit money in a savings account or we take out a loan, there's an interest rate. They tell us what the interest rate is, and that is the nominal interest rate. That is the stated rate of interest on a loan or a deposit, right? So if you go to the bank and they say, "Hey, we're going to pay you 5% interest on this bank account. I wish, right? Well, that 5% that they tell you, that is the stated interest rate, the nominal interest rate. Compare that to the real interest rate. Well, the real interest rate is when we take into account inflation. So we're going to take the nominal rate and adjust the nominal rate adjusted for inflation. Okay? Because remember, that inflation affects your purchasing power. Right? So even though they tell you you're earning 5% on your money, well, when you leave it in there, the prices are also going up over that time you're earning interest. So the purchasing power isn't necessarily 5% greater. Let's go ahead and see how this works in an example and we'll make a conclusion here at the end of the example.
So you only spend your savings on one essential good, mini porcelain figurines. At the beginning of the year, the price of a figurine is $20, and if you were to use your entire $2,000 on figurines, how many figurines would you be able to purchase? Well, this is just some standard arithmetic here. Right? You have $2,000, and we divide it by the $20 price per figurine. So 2,000 divided by 20, that gives us 100 figurines we could purchase at the beginning of the year. Okay? So that's pretty straightforward. We would be able to buy 100 figurines right now. However, let's take interest into account here.
However, suppose you had saved the $2,000, earning 5% interest throughout the year. If the rate of inflation is 2%, how many figurines could you buy at the end of the year? So, notice, now, we've got 2 moving parts. We're going to have $2,000 earning 5% interest, and then we're going to have the price of the figurines growing by 2%. Okay? So let's go ahead and calculate how much money we would have at the end of the year, the new price of the figurines, and then we'll see how many you can afford at the end of the year.
So let's start here with your ending cash. So we'll say the ending cash, once you earn some interest, well, you would have the $2,000, and we are going to multiply it times 1 plus the interest rate, right? Because we're going to take 1, which is the original amount you had, plus the interest rate of 5%. We're going to multiply it by 1.05. Right? The 5 is the interest you're earning. The 1 is the money you already had. So 2,000 times 1.05, that'll get us to the ending amount of money you have. 2,000 times 1.05 tells you you'll have $2,100 at the end of the year, right? And you could have done this two ways. You could have calculated how much interest you get, 2,000 times 5%, that would tell you, okay, you're earning $100 in interest. Either way, we end with a balance of $2,100, and let's see what the ending price is of the figurine.
So the ending price of the figurine, well, we're going to do the same thing here. The price was $20 at the beginning, but it grew by 2%. So we're going to do the same thing, 20 times 1.02 will tell us the price at the end of the year, and that comes out to $20.40. So the price has gone up by 40¢ here, and that is that 2% of inflation. So to find out how many figurines can you buy, we're going to take our amount of money that we have, which would now be $2,100, and divide it by the new price of $20.40. So let's see how many we can actually purchase after saving for a year. $2,100 divided by $20.40 gives us 102.94 figurines. So let's imagine that we could buy parts of a figurine, we would have 102.94 figurines. So how many more figurines are you able to purchase? Well, you're able to purchase 2.94 more figurines, right? You're able to buy an extra 2.94, which is 2.94% of 100, right?
So the real interest rate, what was the real interest rate that you got? Remember, when we think about purchasing power, at the beginning of the year, you were only able to buy 100. Now, you're able to buy 102.94. So you didn't really get a 5% interest rate, right? Because if you had earned 5% interest, well, you should have been able to buy 5% more figurines. However, you're only able to purchase 2.94% more figurines, right? You're not able to buy 105. If you had gotten 5% more figurines, you would have gone from 100 to 105, right? But the change in price is called the Fisher effect, named for the guy who figured it out. The Fisher effect tells us that the nominal rate, so the real interest rate, is going to equal approximately the nominal interest rate minus the inflation rate. So let's see how this works approximately in our problem.
So in our example, we had a real interest rate of 2.94, right? And what was our nominal interest rate? We had 5%, and our inflation rate was 2%. Right? So 5 minus 2 is 3, and that's approximately 2.94. So at low levels of inflation, we can use this formula to approximate the real interest rate. So it's pretty easy. There will be a lot of times on a test where they'll just tell you the nominal rate is this, the inflation rate is that, what is the real interest rate, and you just use this formula, nominal minus inflation rate. Cool? Alright, so that's about it here. Let's go ahead and look at a graph just to see the nominal interest rate over time and let's see what we got here.
So we've got a graph showing, the nominal rate, and the real interest rate in the U.S. over time and what do we see? The difference between the 2 is what we would call the inflation rate, right? The difference between that nominal and the real interest rate is the inflation rate. So, if at any point, we wanted to approximate what the inflation rate is, it's going to be the distance at that point, right? The inflation at that point. But notice what happened in about 2008, 2009 during this recession. What happened? The real interest rate was above the nominal interest rate. Notice the nominal interest rate was basically 0, it was like 0.1% and the real interest rate was above that. How could that happen? Well, that would be if we had negative inflation, right? So we actually had a short period where we went through deflation, where the real interest rate was greater than the nominal interest rate. So what does that mean? That prices were going down over time, right? So you actually had more purchasing power if you waited to spend your money. Even though the nominal interest rate was so low, the prices were decreasing, so you had more purchasing power in the future. So we had short-lived deflation there during the recession, and then you can see, in the past few years, the nominal interest rate didn't really climb and we've had actually a negative real interest rate. That means purchasing power has been decreasing over time. If you were to just sit on money, well, you could buy less stuff because those prices are still going up, right? At this point, there's still inflation of this amount, right? This is still inflation right here causing if you're just sitting on a stack of cash at home, well, that stack of cash is going to be losing value because of the negative real interest rate. Okay? So that's about it. The big hitter here is this formula that we have at the top of the screen right now. Make sure you remember this one because it's easy points on the test when they give you some question like that where you calculate the real interest rate or calculate the inflation rate and they give you the nominal and the real. Cool? Alright, let's pause here and then we'll move on to the next video.
