Question

Suppose that the uncovered interest parity condition holds and the expected exchange rate between the euro and the dollar in one year is 1.50 (€1 = $1.50).

Using the exact formula, determine the current EUR/USD exchange rate when the interest rate is 4% in the Euro area and 5% in the USA. (Answer using 4 decimal pla

Answer 1

Using the uncovered interest parity condition

The forward rate = Spot rate *(1+i_c)/(1+i_b) Where i_c and i_b are interest rates of the two countries

The forward rate is given as 1.50 USD/EUR (1 euro=1.50$) (Or 0.667 EUR/USD)

Using i_c=5% (For usd) and i_b=4% for Euros

We get 1.50=Spot rate* (1.05)/(1.04)

Spot rate =1.50*1.04/1.05=1.4857 USD/EUR (or 0.673 EUR/USD)

Which is the current exchange rate and the condition of interest rate parity

Note: the currency with the lower interest rate i.e. EUR in this case sells at a forward premium(forward rate higher than the spot rate) as 0.673> 0.667 and the one with the higher interest rate sells at a forward discount as 1.4857<1.50 which can be kept in mind while solving to ensure the correct answer.

Hope it helps. Do ask for any clarifications required.