How to use the forward rate agreement calculator
- Enter the notional amount of the agreement.
- Enter the contract rate agreed at the start and the reference rate that applies at the start of the period.
- Enter the number of days in the contract period and choose a 360 or 365 day year.
- Read the settlement the buyer receives or pays, and what the seller does the opposite of.
Formula
Difference at the end = notional x (reference rate - contract rate) x days / year length
Settlement at the start = difference / (1 + reference rate x days / year length)
A positive settlement is received by the buyer and paid by the seller. A negative one is the other way round.
A $5,000,000 agreement over 91 days
With a contract rate of 4.00% and a reference rate of 4.60% on a 360 day year, the interest difference over 91 days is $5,000,000 x 0.60% x 91 / 360 = $7,583.33. That amount would be due at the end of the period, so the settlement paid at the start is discounted at the reference rate: $7,583.33 / (1 + 4.60% x 91 / 360) = $7,496.17.
The buyer, who fixed the cost of borrowing at 4.00%, receives $7,496.17 because rates rose. If the reference rate had been 3.80%, the buyer would pay $2,503.73 to the seller instead.
What a forward rate agreement does
A forward rate agreement fixes an interest rate for a future period without any loan changing hands. The buyer protects against a rise in rates and the seller against a fall. At the start of the period the two sides compare the contract rate with the market reference rate and one pays the other the difference in interest. The notional amount is only used to size the payment and is never exchanged.
Because the interest the difference stands for would only be earned at the end of the period, the settlement is paid early and discounted back by the reference rate. That is why the settlement is smaller than the plain interest difference.
Related rate tools
The contract rate itself often comes from today's spot rates, which the Forward Rate from Spot Rates Calculator can derive. The Simple Interest Calculator shows the interest on the notional for the period, and the Zero Rate Bootstrapping Calculator builds a curve of spot rates from par yields. To see how bond prices move with rates, use the Bond Duration and Convexity Calculator, and for uneven cash flows the XIRR Irregular Cash Flow Calculator.
Assumptions and limits
- Interest is simple interest on the day count you choose.
- The settlement is paid at the start of the period and discounted at the reference rate.
- Real contracts set the day count, the fixing date and the business day rules. Check yours.
- The figures shown are examples and this is not advice about hedging.
Frequently asked questions
Who is the buyer?
The buyer is the side that agrees to pay the contract rate and so gains when market rates rise. The seller gains when they fall.
Why is the settlement discounted?
The settlement is paid at the start of the period, but the interest difference stands for a period that ends later, so it is brought back at the market rate.
Does the notional amount change hands?
No. It is only used to work out the size of the interest payment.
What if the rates are equal?
The settlement is zero, because there is no difference to pay.