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An investor plans to exchange $1,000 into euros now, invest the resulting euros for 12 months, and then exchange the euros back into dollars at the end of the 12-month period. The spot exchange rate is €1·415 per $1 and the euro interest rate is 2% per year. The dollar interest rate is 1·8% per year.
Compared to making a dollar investment for 12 months, at what 12-month forward exchange rate will the investor make neither a loss nor a gain?
i want to know if i understood the concept well, some option answer for this question is very closed for example 1.418 or 1.412
but the answer is 1.418
but this is confused me the if i invest the $1000 in us market i will get $1018 right? and if invested the 1000$ to euros market it will give me after year 1000/1.415 =706.7*(1+0.02) i will get 720.848so to get the exchange rate that gave me $1018 i divided by720.848 the result is ~ 1.412
if i want to check the answer of $1.418 is correct it suppost to when multiply it by 720.848 euro the amount will be 1022 which is different that 1018 while if i used 1.142 i will get the 1018$
The correct forward exchange rate that ensures neither a loss nor a gain is calculated using the interest rate parity formula:
1.415 * 1.02 / 1.018 = 1.418E rate * 1+ I rate 1st / I rate 2nd
1st rate is euroYour calculation of 1.412 is close but does not account for the interest rate parity correctly.
The forward rate of 1.418 ensures that when you convert the future euros back to dollars, you will receive an amount equivalent to the dollar investment, confirming that the investor makes neither a loss nor a gain.
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