# question about simple rate of return

I have a funny question but it confuses me totally!

Say you buy a stock for \$10 and it went up to \$12 that means you gained 20%.

(12-10)/10 =.2

why not (12-10)/12=.1666?

What does each one mean and which is more accurate? I am asking because I got this wrong…

The exchange rate for Australian dollars per British pound (AUD/GBP) was 1.4800 five years ago and is 1.6300 today. The percent change in the Australian dollar relative to the British pound is closest to:

A) appreciation of 10.1%. B) depreciation of 9.2%. C) depreciation of 10.1%.

I worked on an FX desk at DB so i get this stuff

50 to 100 = 100% right but 100 to 50 = -50%

its the idea that when you are long one currency by definition you are short another… if you hold GBP over the period it will appreciate 10.1% 1.63/1.48… so in 5 years you go to exchange it into AUD you will have 10.1% more AUD. the person that held AUD will be getting 9.2% less GBP.

the person HOLDING AUD for 5 years 148,000AUD / 1.63 = 90,797GBP @p5

my return 90,797/100,000 = -9.2% LESS GBP - AUD depreciated RELATIVE TO GBP [B]

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trade @p0 100k AUD / 1.48 = GBP67,567

the person HOLDING GBP for 5 years 67,567GBP x 1.63 = 110,135AUD @p5

return 110,135 / 100,000 = +10.1% MORE AUD