Question

Assume that the one-year nominal (quoted) interest rate is 7% in the U.S. and 6% in Australia. Assume further that you believe in purchasing power parity. You believe the real one-year Interest rate is 2% in the U.S and 3% in Australia. The spot rate of the Australian dollar today is $.80.

A) Determine the expected spot rate of the Australian dollar in one year with respect to the U.S. dollar? Show your work B) You plan to import from Australia and will need 10 million Australian dollars in one year. Determine the expected amount of U.S. dollars to be paid by you for the Australian dollars in one year.

Answer 1

A) first we need to calculate inflation rates of Australia and U.S.

inflation rate of Australia = [(1+nominal interest rate)/(1+real interest rate)] - 1 = [(1+0.06)/(1+0.03)] - 1 = (1.06/1.03) - 1 = 1.029 - 1 = 0.029 or 2.9%

inflation rate of U.S. = [(1+0.07)/(1+0.02)] - 1 = (1.07/1.02) - 1 = 1.049 - 1 = 0.049 or 4.9%

The currency of the country which has higher inflation rate will depreciate because same product which is sold of x will be sold for x+1 in the country with higher inflation.. U.S. has higher inflation rate. so U.S. dollar will depreciate.

expected spot rate = spot rate*[(1+U.S. inflation rate)/(1+Australian inflation rate)]

expected spot rate = $0.80*[(1+0.049)/(1+0.029)] = $0.80*(1.049/1.029) = $0.80*1.0194 = $0.8155

B) expected amount of U.S. dollars = Amount in Australian dollars*expected spot rate

expected amount of U.S. dollars = 10,000,000*$0.8155 = $8,155,000‬