Real and nominal return

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%.