An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 5% and 7% per annum respectively both expressed with continuous compounding). What is the six-month forward rate? Give four decimal places. _ _ _ _ _ _

Question

Quizplus · Accepted Answer

The Answer is To calculate the six-month forward rate, we can use the interest rate parity (IRP) formula, which relates the spot exchange rate, the domestic interest rate, and the foreign interest rate. The formula for the forward rate (F) when interest rates are continuously compounded is:

F = S imes e^{(r_d - r_f) imes t}

Where:
-

F

is the forward exchange rate
-

S

is the spot exchange rate
-

r_d

is the domestic interest rate (continuously compounded)
-

r_f

is the foreign interest rate (continuously compounded)
-

t

is the time in years

Given:
- The spot exchange rate (

S

) is 0.7000
- The domestic interest rate (

r_d

) is 5% per annum, or 0.05 when expressed as a decimal
- The foreign interest rate (

r_f

) is 7% per annum, or 0.07 when expressed as a decimal
- The time (

t

) is six months, which is 0.5 years

Plugging these values into the formula, we get:

F = 0.7000 imes e^{(0.05 - 0.07) imes 0.5}

F = 0.7000 imes e^{-0.01}

F = 0.7000 imes e^{-0.005}

F = 0.7000 imes 0.9950125

(using a calculator for the exponential term)

F \approx 0.6965

Therefore, the six-month forward rate, to four decimal places, is approximately 0.6965.

An Exchange Rate Is 0