Question

Suppose that the one-year interest rate is 5.0 percent in the United States, the spot exchange rate is $1.20/€, and the one-year forward exchange rate is $1.16/€. What must one-year interest rate be in the euro zone?

A.5.0%

B. 6.09%

C. 8.62%

D. None of the above

Formula, calculation, and explanation!

Answer 1

Solution :

As per the Interest rate Differential:

( Forward Rate / Spot Rate ) = [ ( 1 + Interest Rate in Currency A ) / ( 1 + Interest Rate in Currency B ) ] ⁿ

Where n = No. of years

As per the Information given in the question we have

The spot exchange rate is = A/ B = $ / €   = 1.20

The one-year forward exchange rate is = $ / €   = 1.16

Interest rate in Currency A = $ = 5 % = 0.05       

No. of years = 1

Interest rate in Currency B = € = Euro = To find

Applying the above information in the formula we have

1.16 / 1.20 = [ ( 1 + 0.05 ) / ( 1 + x) ]¹

0.9667 = 1.05 / ( 1 + x)

1 + x = 1.05 / 0.9667

1 + x = 1.0862

X = 1.0862 – 1 = 0.862

= 8.62 %

Thus the one year Interest rate in the Euro Zone = 8.62 %

Thus the solution is Option C. = 8.62 %