Sun Bank USA has purchased a 16 million one-year Australian dollar loan that pay

Question

Sun Bank USA has purchased a 16 million one-year Australian dollar loan that pays 13 percent interest annually. The spot rate of U.S. dollars for Australian dollars is $0.6250/A$1. It has funded this loan by accepting a British pound (BP)–denominated deposit for the equivalent amount and maturity at an annual rate of 11 percent. The current spot rate of U.S. dollars for British pounds is $1.6000/£1.

What should the spot rate of U.S. dollars for BPs be at the end of the year in order for the bank to earn a net interest income of $210,000 (disregarding any change in principal values)? (Round your answer to 4 decimal places. (e.g., 32.1616))

Sun Bank USA has purchased a 16 million one-year Australian dollar loan that pays 13 percent interest annually. The spot rate of U.S. dollars for Australian dollars is $0.6250/A$1. It has funded this loan by accepting a British pound (BP)–denominated deposit for the equivalent amount and maturity at an annual rate of 11 percent. The current spot rate of U.S. dollars for British pounds is $1.6000/£1.

What should the spot rate of U.S. dollars for BPs be at the end of the year in order for the bank to earn a net interest income of $210,000 (disregarding any change in principal values)? (Round your answer to 4 decimal places. (e.g., 32.1616))

Explanation / Answer

Loan Amount in USD = 16,000,000 x 0.6250 = $10,000,000
Deposit in GBP = 10,000,000/1.6000 = £6,25,000

Let Y be the spot rate for AS$ at the end of year,
Interest Income at the end of year in USD = A$16,000,000 x 0,13 x Y

Let Z be the spot rate for BPs at the end of year,
Interest Expense at the end of the year = £6,250,000 x 0.11 x Z

For Net interest income of 210,000

16,000,000 x 0,13 x Y - 6,250,000 x 0.11 x Z = 210,000

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