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

Lesson 2: Nominal vs. real interest rates# Calculating real return in last year dollars

In this video we take a slightly different approach to understanding the difference between real and nominal values: find the value of an asset in a previous year's dollars. Created by Sal Khan.

## Want to join the conversation?

- Will the real return in the current year's money and last year's money always be the same, or was that only the case in this example?(12 votes)
- yes. the only difference between current years money and previous years money is inflation rate. The real return in current year's money is adjusted for inflation, so the real return is equal to the return in previous year's money.(19 votes)

- 1:58does last years money have more or less value then this years money?(1 vote)
- I'll restate your question just so your clear on what I'm answering. I think you are asking:
*If I earned $100 last year and kept it in my wallet, would I be able to buy more or less with it if I waited until a year later to spend it.*

That depends on how the value of money has changed. Inflation is the reduction in the value of each dollar. So if prices had**inflated**, you would be able to buy**less**with your $100. If prices had**deflated**, you would be able to buy**more**with your $100.(20 votes)

- at1:13I am confused . why sal do x multiply to 1.02 equals 110 .(6 votes)
- If the inflation rate is 2%, then you multiply last year's money by 100% + 2%, or 102%, to get today's money.

102% in decimal form is 1.02.(11 votes)

- could you describe what real return means?(0 votes)
- Yes I can, but Sal does it better.. Watch previous video(12 votes)

- Why do we need to calculate the real return in last year's money?(4 votes)
- When you say "if you believe the whole CPI index" is that implying a lot of goods and services don't increase in price over the years? How real is inflation(3 votes)
- Sal is saying that the basket of goods that the government uses to calculate inflation may not be a good idea for a basket.(2 votes)

- why we multiply 1.02 instead of .02?(1 vote)
- Because you are trying to find out how much money you have in total, not how much money you earned.(4 votes)

- So what exactly is the formula for calculating the real rate of return?(0 votes)
- (1 + R nominal) = [(1 + R real) * (1 + inflation)] - 1 ==> Nominal Rate of Return in %(3 votes)

- a :55 he said "x multiply 2% but wrote it 1.02?(1 vote)
- yes it 1.00x2%=0.02 then that combined in total is 1.02(2 votes)

- What is Calculate Last Year's Real Dollar Yield?(1 vote)

## Video transcript

Male voice: In the last
video, we were able to calculate the real
return by putting everything in today's dollars. Put
that $100 we invested a year ago in today's dollars, figure out what our actual return
was, our dollar return is in today dollars, then
we got our real return. What I want to think about in this video is how we can do it another way. We can actually put everything in last year's money. We got $110. Let's put $110, of today's money in last year's money. To think about this, we could do a little algebra, or you don't have to do algebra, but maybe that makes it a
little bit more intuitive. There's some amount of money last year, there's some amount of
money, let's call that X, that if we multiply it by the
inflation rate, so if we grow it by 2%, that's going to be worth $110 today. Or, to just solve for X, you divide both sides by 1.02 and we
get the amount of money that if you grow it by
inflation, or that had the same amount of purchasing
power as $110 today, would be 110 divided by 1.02 which is, let me move over to the
right at little bit, this would be 110 divided by 1.02. This would be equal to
$107.8 just roughly, just to round it. This is equal to $107.8. So $110 today buys us
the exact same thing, if you believe the whole CPI Index, as $107.80, maybe I can
even add another digit, 84 cents, would have bought us last year. What is our dollar return
in last year's money? Dollar return in last year's money. Last year's money. Well, we ended up with
$107.84 in last year's money. So 107.84, or $107.84. We had originally invested, in last year's money, $100. We had originally invested $100. So our dollar return is
$7.84, or if you want to calculate the real return, how much did our actual purchasing power increase? Well, we got a $7.84 return
off of a $100 investment, so this is pretty easy to calculate. We once again get to the same
7.8% for the real return.