Suppose that the Australian dollar is worth NZD1.10 and the United States dollar is worth NZD1.75.

a. Calculate the value of the New Zealand dollar against the United States dollar.

b. Using your answer to (a), calculate the cross exchange rate between the United States dollar and the Australian dollar.

c. Let X/Y represent 1 unit of currency X in terms of currency Y. Explain in general why the following rule, called a chain rule, is valid :

AUD/USD = AUD/NZD x NZD/USD

d. Using the formula in (c), check your answer to (b).

e. Using the chain rule in general, show that

AUD/USD = AUD/GBP x GBP/NZD x NZD/USD