Answer:
$7,000
Explanation:
Using the covered interest rate parity formula
No Arbitrage Forward rate = Spot Rate * (1 + RD)/ (1 + RF)
= 1.6 * (1 + 2%)/ (1 + 4%) = 1.6 * 1.02 / 1.04 = $1.57 approximately
However, the actual forward rate = $1.58/€
Hence, there is an arbitrage opportunity.
Suppose an arbitrager borrows 1,000,000 in the United States at 2%.
Thus, after one year, he has to pay back 1,000,000 * (1 + 2%) = $1,020,000
He converts 1,000,000 into Euros at the spot exchage rate of $1.60/€.
Thus he gets 1,000,000/1.6 = €625,000
The arbitrager now invests this money in Germany at 4%.
At the same time, he enters into a forward contract to convert the money that he will get at the end of 1 year into US Dollars at a forward rate of $1.58/€
After 1 year, he gets 625,000 * (1 + 4%) = €650,000
He converts this money into USD at the exchange rate of $1.58/€ (at which he entered the forward contract)
Thus he gets 650,000 * 1.58 = $1,027,000
Amount he has to pay back = $1,000,000 * (1 + 2%) = $1,020,000
Net cash flow for the year through this arbitrage = $1,027,000 - $1,020,000 = $7,000
