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# Calculating real return in last year dollars

AP.MACRO:
MEA‑3.B (LO)
,
MEA‑3.B.1 (EK)
,
MEA‑3.B.3 (EK)

## Video transcript

in the last video we were able to calculate the real return by putting everything in today's dollars put that hundred dollars we invested a year going today's dollars figure out what our actual return was our dollar return is in today's dollars and 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 one hundred and ten dollars let's put one hundred ten dollars let's put one hundred ten of today's money \$100 ten of today's money in in last year's money last years years money and to think about this we could we could do a little algebra or you don't have to do algebra but maybe that makes 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 two percent so if we grow it by two percent that's going to be worth one hundred and ten dollars today that's going to be worth 110 110 dollars 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 1.0 - which is let me scroll over to the right a little bit this would be 110 110 divided by one point zero two so this would be equal to one hundred and seven point eight dollars just roughly just to round it so this is equal to one hundred seven point eight dollars so 110 110 dollars today buys us the exact same thing if you believe the whole CPI index as one hundred and seven dollars and eighty cents and maybe I could even add another digit 84 cents and 84 cents would have bought us last year so what is our dollar return in last year's money dollar return in last year's in last year's money last year's money well we ended up with 107 point eight four dollars and last year's money so 107 point eight for 100 seven dollars and 84 cents and we had originally invested in last year's money \$100 we had originally invested \$100 so our dollar return is seven dollars and 84 cents or if you want to calculate the real return the real return how much did our actual purchasing power increase well we got a 7.8 e four dollar return off of a hundred dollar investment and so this is pretty easy to calculate we once again get to the same seven point eight percent for the real return