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 / £

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