Forward Premium Calculator
Enter the spot rate, the forward rate and the contract length in days to see the forward premium or discount for the period and as a yearly rate.
Updated
Forward Premium Calculator
Our Forward Premium Calculator shows how far a currency forward rate sits above or below today's spot rate. Type the spot rate, the forward rate and the length of the contract in days. It returns the premium or discount for the contract period and the same figure scaled to a full year on a 360-day basis, with a 365-day figure beside it. It suits treasury and finance teams comparing hedging costs, importers and exporters pricing forward cover, and students working through foreign exchange problems.
Quick answer
The annualized forward premium is (forward rate − spot rate) ÷ spot rate × 100 × 360 ÷ days: with a spot rate of 1.2500, a 90-day forward rate of 1.2625, 0.0125 ÷ 1.25 × 100 × 4 = 4% a year.
- Period premium: (forward rate − spot rate) ÷ spot rate × 100.
- Annualized: period premium × 360 ÷ days in the contract.
- Positive result: a forward premium. The forward rate is above spot.
- Negative result: a forward discount. The forward rate is below spot.
What Is a Forward Premium?
A forward premium is the amount by which the forward exchange rate of a currency is higher than its spot rate, written as a percentage of the spot rate. When the forward rate is lower than spot, the gap is called a forward discount.
- Spot rate: the exchange rate for a trade that settles now (normally in two business days).
- Forward rate: the rate agreed today for an exchange on a set future date.
- Contract length: the number of days from the spot date to the forward date.
Both rates must be quoted the same way round, as units of the quote currency for one unit of the base currency. For a rate of 1.2500 US dollars per euro, the euro is the base currency, and a positive result means the euro is at a forward premium against the dollar.
Forward Premium Formula
= (F − S) ÷ S × 100
Annualized premium %
= Period premium × 360 ÷ n
- F: the forward rate.
- S: the spot rate.
- n: the contract length in days.
The first line gives the change over the life of the contract. The second scales it to a year so that contracts of different lengths can be compared with each other and with yearly interest rates. The scaling is simple (not compounded), which is the market convention for forward quotes.
How to Calculate the Forward Premium
The spot rate is 1.2500 and the 90-day forward rate is 1.2625:
= 0.0125
Period = 0.0125 ÷ 1.25 × 100
= 1%
Annualized = 1 × 360 ÷ 90
= 4%
- Find the gap. Forward rate minus spot rate: 1.2625 − 1.2500 = 0.0125.
- Divide by the spot rate. 0.0125 ÷ 1.25 = 0.01, which is 1% over the 90 days.
- Scale to a year. There are 360 ÷ 90 = 4 such periods in a 360-day year, so 1% × 4 = 4%.
Why the Premium Is Annualized
A raw premium only means something next to its time span: 1% over 30 days is a much steeper gap than 1% over a year. Annualizing puts every contract on the same footing. A 30-day forward at 1.1011 against a spot rate of 1.1000 is only 0.1% above spot, yet that works out at 0.1 × 360 ÷ 30 = 1.2% a year.
Forward Premium vs Forward Discount
| Forward vs spot | Result | Called |
|---|---|---|
| Higher | Positive | Premium |
| Lower | Negative | Discount |
| Equal | Zero | At par |
The label belongs to the base currency. If the base currency is at a premium, the quote currency is at a discount for the same contract. Flipping the quote (for example from dollars per euro to euros per dollar) flips the sign of the answer, and the size changes slightly because the division is then by a different spot rate.
Forward Premium Examples
US dollar against the Indian rupee. Spot is 83.25 rupees per dollar and the 90-day forward is 84.10:
= 0.85
Period = 0.85 ÷ 83.25 × 100
≈ 1.0210%
Annualized ≈ 1.0210 × 4
≈ 4.0841%
The dollar is at a forward premium of about 4.08% a year against the rupee.
A forward discount. Spot is 150 yen per dollar and the 180-day forward is 147:
Period = −3 ÷ 150 × 100
= −2%
Annualized = −2 × 360 ÷ 180
= −4%
The result is negative, so the dollar is at a forward discount of 4% a year against the yen.
Forward Premium and Interest Rates
Forward rates are not forecasts. They are set by the gap between the interest rates of the two currencies, a relationship called covered interest rate parity:
÷ (1 + b × n ÷ 360)
Here q is the interest rate of the quote currency and b is the rate of the base currency. With a spot rate of 1.2500, a quote currency rate of 6%, a base currency rate of 2% and 90 days:
≈ 1.2624
Annualized premium ≈ 3.98%
The premium of about 3.98% is close to the 4 point gap between the two interest rates. As a rule of thumb, the currency with the lower interest rate trades at a forward premium and the one with the higher rate trades at a forward discount. If it did not, traders could lock in a risk-free profit.
360 or 365 Days?
This calculator annualizes on a 360-day year, the money market convention for most major currencies, including the US dollar, the euro and the yen. Some currencies, such as the pound sterling, use a 365-day year. The "365-day basis" row gives that version:
365 basis: 1 × 365 ÷ 90
≈ 4.0556%
The period premium is the same either way. Only the yearly figure changes, so use the basis that matches the interest rates you are comparing it with.
What the Result Leaves Out
- Bid and offer spreads. Use mid rates, or the same side for both rates. Mixing a bid with an offer distorts the answer.
- Compounding. The yearly figure is a simple multiple of the period figure, not a compounded rate.
- Exact day counts. Enter the actual number of days in the contract, not a rounded number of months.
- Forecasting. A premium shows the interest rate gap priced into the forward. It does not say where the spot rate will be.
- Costs. Bank margins and fees on a real forward contract are not included.
The result is for education and planning and is not financial advice.
Key Terms
- Spot rate
- The exchange rate for immediate settlement.
- Forward rate
- The exchange rate fixed today for a trade on a future date.
- Forward premium
- The percentage by which the forward rate is above the spot rate.
- Forward discount
- The percentage by which the forward rate is below the spot rate.
- Forward points
- The forward rate minus the spot rate, as quoted by dealers.
- Base currency
- The currency being priced: the "one unit" in an exchange rate quote.
How to Use the Forward Premium Calculator
- Enter the spot rate. Type the current exchange rate, such as 1.2500.
- Enter the forward rate. Type the forward rate quoted the same way round, such as 1.2625.
- Enter the contract length. Type the number of days until the forward date, such as 90.
- Read and copy the result. The annualized forward premium appears as you type, with the working, the premium for the period, the forward minus spot difference, the 365-day figure and whether it is a premium or a discount. Press Copy to copy it, or Clear or Esc to start again.
Example: spot rate 150, forward rate 147 and 180 days. The result is −4%, from (147 − 150) ÷ 150 × 100 × 360 ÷ 180, a forward discount of 2% for the period.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you calculate the forward premium?
Subtract the spot rate from the forward rate, divide by the spot rate and multiply by 100 to get the premium for the period. To annualize it, multiply by 360 and divide by the number of days in the contract.
What is the forward premium if the spot rate is 1.2500 and the 90-day forward rate is 1.2625?
It is 1% for the 90 days and 4% a year. The difference is 0.0125, and 0.0125 ÷ 1.25 × 100 = 1%. Annualized on a 360-day basis that is 1 × 360 ÷ 90 = 4%.
What is the difference between a forward premium and a forward discount?
A currency is at a forward premium when its forward rate is above its spot rate, which gives a positive result. It is at a forward discount when the forward rate is below spot, which gives a negative result.
What does a negative forward premium mean?
It means the forward rate is lower than the spot rate, so the base currency trades at a forward discount. For example, spot 150 and a 180-day forward of 147 give −2% for the period and −4% a year.
Why is the forward premium annualized?
Annualizing lets you compare contracts of different lengths and set the premium against yearly interest rates. A 0.1% premium over 30 days and a 1.2% premium over 360 days are the same pace.
Does the calculator use 360 or 365 days?
The main result uses a 360-day year, the convention for most major currencies. A separate row shows the same premium on a 365-day basis, which is used for currencies such as the pound sterling.
Why do forward premiums exist?
Because the two currencies earn different interest rates. Under covered interest rate parity the currency with the lower interest rate trades at a forward premium that roughly equals the interest rate gap, so that no risk-free profit is available.
Does a forward premium predict the future exchange rate?
Not reliably. The forward rate reflects the interest rate gap between the two currencies, not a forecast. Spot rates often move differently from what the forward implied.
Is the Forward Premium Calculator free?
Yes. It is free to use, with no sign-up and no limit on how many times you use it.
Sources
- Corporate Finance Institute. Forward Premium.
- Wikipedia. Forward exchange rate.
- WallStreetMojo. Forward Premium.
- Corporate Finance Institute. Covered Interest Rate Parity (CIRP).
- Wikipedia. Interest rate parity.
- Wikipedia. Day count convention.
Try our Forward Premium Calculator to turn any spot and forward quote into a yearly premium or discount.