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Derivatives forwards and exchange rates The current US$/Euro exchange rate is 1.4000 dollar per Euro. The 6-month forward exchange rate is 1.3950. The 6-month US$

Derivatives forwards and exchange rates

The current US$/Euro exchange rate is 1.4000 dollar per Euro. The 6-month forward exchange rate is 1.3950. The 6-month US$ interest rate is 1% per annum continuously compounded. Estimate the 6-month Euro interest rate.

I have the answer its below. My problem is I don't understand the natural log process and how to get R. Not sure where the 2 came from before the ln.

.Current USD/Euro rate is 1.4000 $/Euro.

6-month forward exchange rate is 1.395.

6-month USD interest rate is 1%

If the 6-month Euro interest rate is r, then

1.395 = 1.400e(0.01-r)x0.5

So 0.01 -r = 2ln(1.395/1.400) = -0.00716

Hence, r = 0.01716

The 6-month Euro interest rate is 1.716%

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