We are valuing an FRA for someone who is receiving fixed interest rate payments and who is paying floating interest rate payments.

## a. Value of an FRA (zero coupon rate calculated on a discrete basis)

Where, L is the principal amount

R_{K} is the fixed interest rate

R_{F} is the forward interest rate assuming that it will equal the realized benchmark or floating rate for the period between times T_{1} and T_{2}

R_{2} is the zero coupon rate for a maturity of T_{2}. In this instance it has been calculated on an effective annual discrete time basis.

If principal amount, L, is 1000, and we are to receive a fixed interest rate of 15% annually compounded on this amount between the end of year 3 and the end of year 4 and pay a floating rate of 12.5% annually compounded, and the effective annual 4- year zero coupon rate is 12%, then the Value of the Forward Rate Agreement will be:

V_{FRA} =1000 × (15% – 12.5%) × (4 – 3) ÷ (1+12%)^{4 }= 15.89

You may calculate this in EXCEL in the following manner:

## b. Value of an FRA (zero coupon rate calculated on a continuously compounded basis)

In this instance the zero coupon rate has been calculated on a continuously compounded basis.

Again if principal amount, L, is 1000, and we are to receive a fixed interest rate of 15% annually compounded on this amount between the end of year 3 and the end of year 4 and pay a floating rate of 12.5% annually compounded, and the continuously compounded 4- year zero coupon rate is 12%, then the Value of the Forward Rate Agreement will be:

V_{FRA} =1000 × (15% – 12.5%) × (4 – 3) × e^{-0.12×4 }= 15.47

You may calculate this in EXCEL in the following manner:

## c. How to calculate Forward Exchange Rates

### i. Interest Rates compounded on a discrete basis

Where

r is the risk free rate of the domestic currency

r_{f} is the risk free rate of the foreign currency

Suppose that the 1-year interest rates in USD and Pakistan are 2% and 10% respectively. The spot exchange rate is USD 1 = PKR 90.77. The one-year forward exchange rate will be:

F_{0} = 90.77×[(1+10%)/(1+2%)]^{1 }= 97.89

You may calculate this in EXCEL in the following manner:

### Interest Rates compounded on a continuous basis

Suppose that the 1-year interest rates in USD and Pakistan are 2% and 10% respectively. The spot exchange rate is USD 1 = PKR 90.77. The one-year forward exchange rate will be:

F0 = 90.77 × e^{(0.1-0.02) × 1 }= 98.33

You may calculate this in EXCEL in the following manner: