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Let R_1 be the change rate from RMB to US dollars when transferring money from China to U.S., and R_2 the rate from US dollars to RMB when transferring money from U.S. to China.

Are R_1 and R_2 exactly reciprocal to each other? i.e. is R_1 = 1/R_2? If not, why?

Does the relation between R_1 and R_2 depend on the specific banks in China and in U.S.? For example, R_1 is from bank C1 in China to bank A1 in U.S, and R_2 is from bank A2 in U.S. to bank C2 in China.

Are the transfers for both directions done in banks in china, or in banks in U.S.?

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    R_1 and R_2 aren't likely to be reciprocals as most places that do conversions will add a bit of a buffer to the rates they use and thus if you took $1 US and converted to a foreign currency and converted it back you may end up just under a dollar,e.g. 99.9 cents which may get rounded back to a whole dollar but isn't exactly where you started. – JB King Oct 15 '13 at 23:05
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Are R_1 and R_2 exactly reciprocal to each other?

No for a normal day to day transaction they are not equal.
A Bank in China is operating in RMB. USD for a Bank in China is like goods. It will buy USD from you at a cheaper rate and sell it to someone at a higher price.
So there are 2 rates, Bank Buy Rate of R_1Buy and Bank Sell Rate of R_1Sell. The difference is the spread and the profit / money Banks make from this transaction.

For a Bank in US similarly there is a Bank Buy Rate of R_2Buy and Bank Sell Rate of R_2Sell.

In theory R_1Buy would be inverse of R_2Sell. Similarly R_1Sell would be inverse of R_2Buy. However there would difference due to price fluctuations and demand and supply considerations.

Now when you go to a Bank in China, you get a R_1Sell rate, because Bank is Selling USD to you. This is same as R_2Buy in US as the Bank is Buying RMB. While on the other side when you transfer money from US to China, the Bank in US is selling you RMB and the rate would be R_2Sell and this would be same as Bank in China Buying USD from you, rate of R_1Buy.

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