exchange rate

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 720.848

so 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 $1.418 is correct it suppost to when multiply it by 720.848 euro the amount will be 1022 which is different that 1018 while if i used 1.142 i will get the 1018$