Question

The annual interest rate in Australia and the U.S. are 4% and 1% respectively. The forward exchange rate of US$ against AU$ (F AU$ per US$) is of 5% premium relative to the spot exchange rate (S AU$ per US$), i.e., F = S*(1+5%). According to Interest Rate Parity Theorem, is US$ relatively undervalued or overvalued with respect to AU$ in the spot market if the forward rate is correct?

Answer 1

Let the spot rate be x
Forward Rate AU$/US$= x * (1+5%) = 1.05x
1 Year Interest Rate on AU Dollar = 4%
1 Year Interest Rate on U.S. Dollar = 1%

As per Interest Rate parity forward rate is calculated as

where:
id=The interest rate in the domestic currency or the base currency
if=The interest rate in the foreign currency or the quoted currency
S=The current spot exchange rate
F=The forward foreign exchange rate​

We use the equation to calculate the should be spot rate.

Using the formula :
1.05x/S = (1 + 0.04)/(1+ 0.01)
1.05x/S = 1.04/1.01
1.05x/S = 1.0297
S = 1.05x/1.0297
S = 1.0197x

Since the should be spot rate (1.0197x) should be more than the prevailing spot rate (x), US $ is undervalued with respect to AU $ in the spot market.