Problem $1.$

Suppose that the term structure of risk$-$free interest rates is flat in the United States and Australia. The USD interest rate is $7\%$ per annum and the AUD rate is $9\%$ per annum. The current value of the AUD is $0\mathrm{.}62$ USD. Under the terms of a swap agreement, a financial institution pays $8\%$ per annum in AUD and receives $4\%$ per annum in USD. The principals in the two currencies are $$12$ million USD and $20$ million AUD. Payments are exchanged every year, with one exchange having just taken place. The swap will last two more years. What is the value of the swap to the financial institution? Assume all interest rates are continuously compounded.