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10% increase and 10% decrease

hi
in the probability distribuitions they are saying that a 10% increase and a 10% decrease would bring the price to the initial level. how is that possible. for example

initial price = 50$
10% increase = (100+10)*50/100 = 55
now the new price = 55
at this point a 10% decrease is 10% of 55 = 5.5 and so the new price = 49.5

similarly if we do the 10% decrease first and then do a 10% increase on the new price then we get the same 49.5 again.

but the book says 1.1*50/1.1 = 50

why would a 10 percent decrease use division when in fact it should be

1.1 * 50 - 1.1*50*10/100 = 1.1 * 50 [100 - 10]/100 = 1.1 * 50 * 90 / 100

there is no way i can see how 90/100 would equal 1/1.1 (which ignores a good rounding error) and then bring the final value to 50 instead of 49.5

this is really killing me. i would sincerely appreciate a quick and compelling response.

thanks
kiran

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This is discounting question. you see, if your required rate is 10%, what should be ending value that you get into that.

50*1.1=55

Aternatively, if you get 55 at the end, what you should invest to get 10% return. You need to discount

55/1.1 = 50

Muhammad Shahid