Calculating real return in last year dollars | Inflation | Finance & Capital Markets | Khan Academy

ruticker 07.03.2025 23:39:00

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In the last video, we were able to calculate the real return by putting everything in today's dollars. We took that **$100** we invested a year ago and figured out what our actual return was in today's 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. So, 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, and 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. To 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: \[ X = \frac{110}{1.02} \approx 107.84 \] So, **$110** today buys us the exact same thing, if you believe the whole CPI index, as **$107.84** last year. Now, what is our dollar return in last year's money? Well, we ended up with **$107.84** in last year's money, and we had originally invested in last year's money **$100**. So, our dollar return is: \[ 107.84 - 100 = 7.84 \] Or, if you want to calculate the real return, how much did our actual purchasing power increase? We got a **$7.84** return off of a **$100** investment. This is pretty easy to calculate, and we once again get to the same **7.84%** for the real return.

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