How are currency exchange rates calculated?

Question

The US Dollar is declining in value against the British Pound and the Euro, but the decline versus the Euro is greater.
If US interest rates are reset lower, I am told that the value of the Dollar versus the other currencies declines further.
These exchange rates are calculated to four decimal places, indicating significant precision.
If the Chinese Yuan is set higher than it currently is, what will that do to the Dollar versus the Pound and the Euro?

Answer 1

Exchange rates are not calculated the are determined by the currency exchange markets where traders by and sell currencies. see FOREX.
The theory predicts that that the demand for dollars is dependent on the interest investors can get on dollar denominated bonds, so a lower interest rate decreases the demand and would lower the "price" of the dollar, but the amount of the decrease is a rough estimate.

Answer 2

calculate a currency exchange rate

Answer 3

Yuan maybe unchange to dollar and other currencies if Chinese central bank keeps on selling more bonds to commercial banks to buy US bonds, but dollar maybe downgraded to other currencies alone in certain condition.

In short term, can use this common equation to determine 90 days exchange rate over dollar adjust with interest rate affect: Ff= (1+rf)Sf/(1+r$), Sf=spot rate