Question

Assume the following information regarding U.S. and European annualized interest rates: ​ Currency Lending Rate Borrowing Rate U.S. Dollar ($) 6.73% 7.20% Euro (€) 6.80% 7.28% ​ Trensor Bank can borrow either $20 million or €20 million. The current spot rate of the euro is $1.13. Furthermore, Trensor Bank expects the spot rate of the euro to be $1.10 in 90 days. What is Trensor Bank's dollar profit from speculating if the spot rate of the euro is indeed $1.10 in 90 days?

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Answer 1

1. Borrow €20 million.

2. Convert the €20 million into dollar

= Borrowed Amount in euro * Current Spot Rate

= €20,000,000 * $1.13 = $22,600,000.

3. Invest the $22,600,000 at an annualized rate of 6.73% for 90 days.

= Amount in dollars * [1 + {USD lending rate * (days of instrument/360)}]

= $22,600,000 * [1 + {6.73% * (90/360)}]= $22,600,000 * 1.016825 = $22,980,245

4. Determine euros owed = Borrowed amount in euros * [1 + {Euro Borrowing rate * (days of instrument/360)}]

= €20,000,000 * [1 + {7.28% * (90/360)}] = €20,000,000 * 1.0182 = €20,364,000.

5. Determine dollars needed to repay euro loan = Euros owed * Spot rate in days

= €20,364,000 * $1.10 = $22,400,400.

6. The dollar profit = $22,980,245 - $22,400,400 = $579,845