Question

what is the three-month forward rate for gbp/usd if the spot rate is 1.35 and the three-month libor rates in the uk and us are 0.4% and 0.95%, respectively?]

Answer 1

The three-month forward rate for GBP/USD, calculated using the Interest Rate Parity formula with a spot rate of 1.35, UK LIBOR of 0.4%, and US LIBOR of 0.95%, is approximately 1.3442 GBP/USD.

Step-by-step explanation:

To calculate the three-month forward rate for GBP/USD, given the spot rate and the three-month LIBOR rates for both the UK and US, we use the Interest Rate Parity (IRP) formula, which connects the spot rate, interest rates of two different countries, and the forward exchange rate.

The formula for finding the forward exchange rate is:

Forward Rate = Spot Rate x (1 + Interest Rate of Domestic Currency) / (1 + Interest Rate of Foreign Currency)

Where:

• 'Domestic currency' is the investor's perspective. In this case, it's GBP.
• 'Foreign currency' is USD.

Using the provided rates:

• Spot Rate = 1.35 GBP/USD
• UK LIBOR = 0.4%
• US LIBOR = 0.95%

The calculation would be:

Forward Rate = 1.35 x (1 + 0.004) / (1 + 0.0095)

Forward Rate = 1.35 x 1.004 / 1.0095

Forward Rate ≈ 1.3442 GBP/USD

Therefore, the three-month forward rate for GBP/USD, given a spot rate of 1.35, a UK LIBOR of 0.4%, and a US LIBOR of 0.95%, would be approximately 1.3442.

Answer 2

The three-month forward rate for GBP/USD can be calculated using the interest rate differential between the UK's and the US's LIBOR rates. Using the formula, the student can input the spot rate and the respective LIBOR rates to determine the adjusted forward rate for the currency pair.

Step-by-step explanation:

The student is asking how to calculate the three-month forward rate for GBP/USD based on the given spot rate and the three-month LIBOR rates in both the UK and the US. To determine the forward rate, we need to take into account the interest rate differentials between the two currencies in question. The forward rate is adjusted from the spot rate in proportion to the interest rate differential for the period.

The formula to calculate the forward rate (F) is:

F = S × (1 + r_{domestic} × T) / (1 + r_{foreign} × T),

where S is the spot rate, r_{domestic} and r_{foreign} are the domestic and foreign interest rates, respectively, and T is the time to maturity (in years).

In this case, the domestic currency is USD and the foreign currency is GBP. Thus, we plug the values:

F = 1.35 × (1 + 0.0095 × 0.25) / (1 + 0.004 × 0.25),

which simplifies to:

F = 1.35 × (1 + 0.002375) / (1 + 0.001),

F = 1.35 × 1.002375 / 1.001,

When you perform the calculation, you will get the three-month forward rate for GBP/USD.