Question

Sun Bank USA has purchased a 32 million one-year Australian dollar loan that pays 16 percent interest annually. The spot rate of U.S. dollars for Australian dollars (AUD/USD) is $0.625/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 14 percent. The current spot rate of U.S. dollars for British pounds (GBP/USD) is $1.60/£1.

a. What is the net interest income earned in dollars on this one-year transaction if the spot rate of U.S. dollars for Australian dollars and U.S. dollars for BPs at the end of the year are $0.588/A$1 and $1.650/£1, respectively? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your final answer to the nearest whole number. (e.g., 32))
b. 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 $290,000 (disregarding any change in principal values)? (Round your answer to 5 decimal places. (e.g., 32.16161))

Answer 1

a). Amount in $ = Amount in A$ * Spot rate

= A$32,000,000 * ($0.625 / A$1) = $20,000,000

Deposit amount = Loan amount / Rate of U.S dollar for Euro

= $20,000,000 / $1.60/£1 = £12,500,000

Interest Income = Loan * Rate of interest * Spot rate

= A$32,000,000 * 16% * $0.5880/A$1 = $2,257,920

b). Net Cost of Deposit = Interest Income - $290,000

= $2,257,920 - $290,000 = $1,967,920

Pound = Net cost / Interest

= $1,967,920 / (£12,500,000 x 0.14) = $1,967,920 / £1,750,000 = $1.12453 / £