28.07.2022 - 07:33

# 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 depo

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. 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$0.5880/A$1 and$1.5500/ 1, respectively? (Negative amount should be indicated by a minus sign.)

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 $270,000 (disregarding any change in principal values)? (Round your answer to 4 decimal places. (e.g., 32.1616)) Answers (1) • April 8, 2023 в 07:10 a. The net interest income earned in dollars on this one-year transaction can be calculated as follows: - First, convert the 16 million Australian dollar loan to U.S. dollars using the spot rate: 16 million A$ * $0.6250/A$1 = $10 million - Next, calculate the interest income from the Australian dollar loan:$10 million * 13% = $1.3 million - Convert the BP deposit to U.S. dollars using the spot rate: 16 million BP *$1.6000/1 = $25.6 million - Calculate the interest expense on the BP deposit:$25.6 million * 11% = $2.816 million - The net interest income earned in dollars on this transaction is the difference between the interest income and interest expense:$1.3 million - $2.816 million = -$1.516 million Therefore, the net interest income earned on this one-year transaction is -$1.516 million, indicating a loss. b. To earn a net interest income of$270,000, the interest income from the Australian dollar loan should cover the interest expense on the BP deposit and leave a surplus of $270,000. Using the same calculations as in part a, we can set up the following equation:$10 million * x% - $25.6 million * 11% =$270,000 Solving for x, we get: x% = ($270,000 +$25.6 million * 11%) / $10 million x% = 37.35% Therefore, the spot rate of U.S. dollars for BPs at the end of the year should be 37.35% higher than the initial spot rate of$1.6000/1, which is $2.1964/1. Rounded to 4 decimal places, the answer is$2.1964/1.
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