Question

An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 0% and 7% (both expressed with continuous compounding). What is the six-month forward rate?

A) 0.6527

B) 0.6759

C) 0.70

D) 0.7508

Answer 1

To find the six-month forward rate with a spot rate of 0.7000 and interest rates of 0% (domestic) and 7% (foreign), we use the IRP formula. Calculating using continuous compounding for six months, the result is approximately 0.6759. Therefore, the correct option is B.

Step-by-step explanation:

To calculate the six-month forward rate given an exchange rate of 0.7000 and a differential in continuous compounding interest rates (domestic at 0% and foreign at 7%), we can use the Interest Rate Parity (IRP) formula: F = Se^(d - f)t, where F is the forward exchange rate, S is the spot exchange rate, d and f are the domestic and foreign interest rates respectively, and t is the time in years. For this problem:

• S = 0.7000
• d = 0%
• f = 7%
• t = 0.5 years (since we are looking for the six-month forward rate)

The formula becomes F = 0.7000e^(0 - 0.07 × 0.5). Calculating this, you get:

Forward Rate F ≈ 0.7000 × e^(-0.035) ≈ 0.7000 × 0.9659 ≈ 0.6761

Thus, the closest answer to the six-month forward rate from the options provided is B) 0.6759.