Question

You can buy or sell the £ spot at $1.98 to the pound. You can buy or sell the pound one-year forward at $2.01 to the pound. If U.S. annual interest rates are 5 percent, what must be the approximate one-year British interest rate if interest rate parity holds?

Answer 1

The approximate British interest rate is determined using interest rate parity. By equating the ratio of the forward rate to the spot rate with the ratio of the interest rates and solving for the British rate, the answer is found to be approximately 6.62%.

Step-by-step explanation:

To determine the approximate British interest rate, we must use the concept of interest rate parity, which holds that the difference in interest rates between two countries is equal to the differential between the forward exchange rate and the spot exchange rate.

The one-year forward rate is $2.01/£, and the spot rate is $1.98/£. According to the interest rate parity:

(1 + i_£) = (Forward rate / Spot rate) * (1 + i_$)

where i_£ is the British interest rate and i_$ is the U.S. interest rate.

Let's plug in the given values:

(1 + i_£) = (2.01/1.98) * (1 + 0.05)

(1 + i_£) = (2.01/1.98) * 1.05

Now we calculate the right-hand side:

(1 + i_£) ≈ 1.066162

Subtract 1 from both sides to find the British interest rate:

i_£ ≈ 0.066162 or approximately 6.62%

The approximate one-year British interest rate, if interest rate parity holds, should be around 6.62%.