Assume that the USD / AUD exchange rate (the value of 1 USD measured in AUD = how many AUD you have to pay to buy 1USD) has a volatility of =6% p.a. and a current price of =$2 AUD (so we pay $2 AUD to buy 1 USD) and that the risk free rates of interest are q=2% in the US and r=4% in Australia.

Compute the prices of "at the money" put options on the USD with maturities of 0.5, 1.00, 1.5 & 2.0 years using the black scholes model. At the money means the exercise price X for the option is the same as the spot price S of the asset the option is defined over.

The formula is P= X * e^-rT * N(-d₂)-S*e^^-rT*N(-d₁),where,

d₁= ln(S*e^-qt/X*e^-rT)/(T) + T

d₁= d1- T