Macroeconomics - Currency Question

The spot rate on the New Zealand Dollar (NZD) is NZD/USD 1.4286 and the 180-day forward rate is NZD/USD 1.3889. This difference means:

A. Interest rates are lower in the US than in NZ

B. Interest rates are higher in the US than in NZ

C. It takes more NZD to buy one USD in the forward market than in the spot market

I thought, as it takes less NZD to buy 1 USD in the future, the NZ interest rate must be higher, as the currency is stronger in the future than the USD. That’s not the correct answer though.

Any ideas?

Interest rate parity: the currency with the higher risk-free rate depreciates vis-à-vis the currency with the lower risk-free rate; the currency with the lower risk-free rate appreciates vis-à-vis the currency with the higher risk-free rate.

In your example, the USD is trading at a forward discount. Thus, US interest rates must be higher than NZ interest rates (option B).

Essentially, the covered interest rate parity states: what we gain through a higher interest rate, we lose through a forward discount. Otherwise, there are arbitrage opportunities.

Here is a simple example: suppose USD and NZD are currently trading at parity and NZ interest rate is 6% and US interest rate is 4%. We would expect NZD to trade at a forward discount. Suppose this is not the case and NZD is trading at parity in the one year forward market. This represents an arbitrage opportunity: an investor can borrow 100 USD at 4%, convert this sum into 100 NZD, invest at 6% and in one year receive 106 NZD. He will then convert the 106 NZD into 106 USD using the forward contract, pay off the 100 USD principal and 4 USD interest, and generate a risk-free profit of 2 USD.

To prevent this arbitrage opportunity, NZD should have been trading at a forward discount due to higher NZ interest rates.