Question

1.The current U.S. dollar-yen spot rate is 102¥/$. If the 90-day forward exchange rate is 101¥/$ what is the forward exchange premium or discount for ¥$.

2.Assume the current U.S. dollar-British spot rate is 0.71£/$. If the current nominal one-year interest rate in the U.S. is 2.7% and the comparable rate in Britain is 3.9%, what is the approximate forward exchange rate for 180 days?

Answer 1

Solution 1).

Current Spot Exchange Rate is 102¥/$. (i.e $ 1 = ¥102)

90-days Forward Exchange Rate is 101¥/$. (i.e $ 1 = ¥101)

USD is at a discount since ¥ value is decreasing from ¥ 102 to ¥ 101 per dollar

The forward exchange discount ¥/$ : (Difference in value/spot rate)* 360/90

The forward exchange discount ¥/$ : [(102-101)/102]* 360/90

The forward exchange discount ¥/$ : 0.0392 or 3.92%

(Note: The yearly days has been taken as 360 in the solution, alternatively 365 days could also be taken)

Solution 2).

The current Spot Rate is 0.71£/$.(i.e. $1= 0.71£)

One-year U.S. interest rate is 2.7% and the rate in Britain is 3.9% & time is 180 days

We know that:

(Forward rate £/$) / (Spot Rate £/$) = (1+ Interest £) / (1+ Interest $)

(Forward rate £/$) / (0.71 £/$) = (1+ 0.039*180/360) / (1+ 0.027*180/360)

(Forward rate £/$) = (1+ 0.039*180/360) / (1+ 0.027*180/360) * (0.71 )

(Forward rate £/$) = (1.0195) / (1.0135) * (0.71)

(Forward rate £/$) = 0.714 or 0.72

Hence, the approximate forward exchange rate for 180 days is 0.72£/$