Monday, January 12, 2009

currency exchange

i have 22000 JPN after Japan Trip. the rate is now 1000 JPN to 8.3HKD. 

the clerk tell  me it is around 2000HKD, need to pay 50HKD as a fee. but she also tell me, if i have other currency more than 3000HKD in total, then free of charge.

i ask her.

can i use 3000HKD to RMB, than change those RMB and JPN to HKD?

currently, 

3000HKD -> 2,646.0553 RMB

22000JPN  -> 1,915.78 HKD

2646 RMB  -> 2999.99 HKD

and 2646.05 RMB + 22000JPN  -> 4,915.77 HKD

therefore, i don't need to pay any fee!!!

i am so suprised that i suddenly come up with this trick. :P

in this way, let us calculate how much money exhange will really cost some fee.

Let 
R(HKD, RMB) be  rate from HKD to RMB
RMB = R(HKD,RMB) HKD..........(1)
R(RMB,HKD) be the rate from HKD to RMB
HKD = R(RMB, HKD) RMB.........(2)

this 2 rate should be only different by some among : d 

R(HKD,RMB)* R(RMB,HKD)  + d = 1
d can be positive or negative. 

the lost is 
 HKD -  R(RMB, HKD) R(HKD,RMB) HKD =  d * HKD

currently, the d is less than 0.0001 therefore, if i exchange more than 
 d * HKD >= 50

=> HKD > 500,000 at least (apprx.)

, then i have to pay 50HKD fee for the exchange. 
however, if i exhange more than 3000HKD, i don't have to pay. 
therefore, we never need to pay. 

i suggest, if the bank really like to charge some fee, 
they need to set each exhange will be free for more than 500,000 HKD.
if so, no body can play trick. 
but all about only for d is positive. 
if d is negative, i really earn money from this exchange!

may be, just forget the fee.

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