Calculating a forward rate: the formula, a full worked example, and the mistake to avoid
A forward rate is not a forecast: it is anchored on spot and the interest-rate differential. The formula, applied step by step, what it does not tell you, and how to deduce what your bank is taking.
Search for « forward rate calculation » and you will find two families of pages. On one side, consumer currency converters, which can only do a spot conversion. On the other, academic formula pages: accurate, but with no usable example and no word on what the result is for.
What is missing in between is what a finance team actually needs: the formula, a worked case you can redo, and above all the reason for doing the calculation — knowing whether the rate you are quoted is fair.
1. What a forward rate really is
A forward rate is the rate you commit to today for an FX transaction that will take place at a future date. The first question everyone asks is: how does the bank know where EUR/USD will be in six months?
It does not know, and it does not need to: a forward rate is not a forecast of the future spot. It is anchored on an arbitrage relationship between spot and the interest rates of the two currencies. That does not mean it reduces to a calculation — section 4 covers what the formula leaves out.
Imagine you have to deliver USD 1 million in six months. A bank can guarantee that without taking any bet: it borrows euros today, converts them into dollars at today's rate, places those dollars for six months, and delivers them at maturity. Its cost is known in advance — it is the gap between the two interest rates. The forward rate is simply that operation, expressed as a price.
Which is why a forward rate can be estimated, and why a bank justifying an unfavourable rate by « market expectations » is describing its own product poorly. The calculation does not reproduce the price to the last point, but it gives the right order of magnitude — and that is already what most companies lack.
2. The formula
For a pair whose first currency is the base and second the quote currency — in EUR/USD, the euro is the base and the dollar the quote:
| Input | What it is | Where to find it |
|---|---|---|
| Spot rate | The market mid rate at the time of the calculation | Public market data |
| Quote-currency rate | The dollar funding rate over the period — not the Fed's policy rate | Funding curve, matching maturity |
| Base-currency rate | The euro funding rate over the same period — not the ECB's policy rate | Funding curve, matching maturity |
| n | The number of days to maturity | Your schedule |
The forward rate is the spot rate multiplied by the ratio of the two currencies' compounding factors: spot × (1 + quote rate × n/360) ÷ (1 + base rate × n/360).
3. The worked example, to redo yourself
An exporter expects to receive USD 1,000,000 in six months. It wants to fix today the euro amount it will get. Its bank quotes a rate. Is it fair?
The calculation runs in three steps. First compound each currency over the period: the dollar gives 1 + 0.0410 × 180/360 = 1.0205; the euro gives 1 + 0.0215 × 180/360 = 1.01075. Then divide the first by the second, which gives 1.009646. Finally multiply the spot rate by that ratio.
| Step | Calculation | Result |
|---|---|---|
| Compounding the dollar | 1 + 0.0410 × 180/360 | 1.020500 |
| Compounding the euro | 1 + 0.0215 × 180/360 | 1.010750 |
| Ratio of the two | 1.020500 ÷ 1.010750 | 1.009646 |
| Forward rate | 1.0850 × 1.009646 | 1.0955 |
| Forward points | 1.0955 − 1.0850 | +105 points |
The reference forward rate is therefore 1.0955. If the bank quotes 1.1010, the gap is 0.50 % — because in EUR/USD a higher rate means fewer euros per dollar, so less for the exporter. On the million dollars, that is about EUR 4,560 between the reference rate and the rate quoted.
Without the calculation, 1.1010 is just a number: you can neither accept nor challenge it. With it, 1.1010 becomes a 0.50 % gap to a reference you can recompute, and the conversation with the bank changes in nature. Most of that gap is the bank's remuneration — but not all of it, and the next section explains why.
4. What the formula does not tell you
The formula gives the theoretical anchor of a forward rate. It does not give the price at which the market actually trades, and presenting the two as identical would be dishonest. Three gaps separate them.
- 1Forward points are quoted, not merely derived
Premium and discount are not a by-product of the calculation: they trade on the FX swap market, with their own bid and offer. Like any quoted instrument, their level reflects the supply of and demand for funding in each currency at that maturity, not just a rate differential frozen in a table.
- 2The rates involved are not policy rates
What goes into the calculation is the rate at which each currency is actually funded over the period concerned. ECB and Fed policy rates steer those rates but do not set them. Putting a policy rate into the formula gives an approximate result, never the right one.
- 3The cross-currency basis
The residual gap between the theoretical forward rate and the rate actually quoted has a name: the cross-currency basis. It reflects the fact that borrowing dollars against euros does not cost exactly what interest-rate parity predicts. It is small on major pairs in calm markets, and widens markedly on illiquid currencies, long maturities and across quarter-ends and year-ends.
So the gap between your calculation and your bank's quote is not, to the euro, its margin: it also contains the market's bid-offer and the basis. On a major pair at a common maturity, those two stay small next to the commercial margin, and the gap remains overwhelmingly margin. On an illiquid currency, a distant maturity or a year-end, they no longer do. The calculation remains the right tool to spot an abnormal quote and open the discussion; it is not a measurement to the basis point, and it should not be presented as one to your banker.
5. Premium and discount: reading the direction the right way round
When the forward rate is above spot, the currency is said to trade at a premium; when it is below, at a discount. The direction follows mostly from the rate differential: the higher-yielding currency trades at a discount against the other.
In our example, dollar rates exceed euro rates: the dollar is at a discount, meaning EUR/USD rises forward, and an exporter selling dollars forward gets fewer euros than at spot. That is neither a penalty nor an unfavourable expectation — it is the exact counterpart of the fact that it could have placed those dollars at a higher rate for six months.
The most common mistake is to compare the forward rate quoted with today's spot rate and conclude the bank is expensive. Those two rates are not comparable: the gap between them is interest rate, not margin. The only comparison that means anything is between the rate quoted and the reference forward rate for the same maturity.
6. The three pitfalls of the calculation
- 1Taking the wrong spot rate
The starting point is the market mid rate, not the rate displayed by your bank — which already contains a margin. Starting from the latter means measuring the margin from a price that already includes it, and therefore measuring nothing at all.
- 2Using the wrong rate maturity
The rate must match the exact duration of the transaction. Applying a 12-month rate to a 3-month hedge produces a gap that has nothing to do with the bank's margin.
- 3Forgetting the day-count convention
Not all money markets use 360 days: sterling counts in 365. On a short maturity the error stays modest; on a long one it becomes the same order of magnitude as what you are trying to measure.
7. From calculation to negotiation
The calculation is not an end in itself. What it produces is a number you can put on the table, and that is what changes a banking relationship.
- Ask for the quote and note the time. A quote with no timestamp cannot be checked.
- At the same moment, note the market mid rate and the two interest rates for that maturity.
- Apply the formula and compare. You get the gap as a percentage of notional.
- Repeat on three or four transactions before opening the discussion: a one-off gap can be explained, a recurring one is a pricing condition.
- Present the record rather than a general request. A bank does not renegotiate a line its client cannot quantify.
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Frequently asked questions
The questions finance departments ask most often on this topic
What is the forward rate formula?
Forward rate = spot × (1 + quote-currency rate × n/360) ÷ (1 + base-currency rate × n/360), where n is the number of days to maturity. In EUR/USD, the base currency is the euro and the quote currency the dollar. The rates to use are each currency's funding rate over the period, not central-bank policy rates. This formula gives the theoretical anchor of a forward rate, not the exact price at which the market trades: forward points are themselves quoted, with a bid and an offer.
Is a forward rate a forecast of the future spot rate?
No, and this is the most widespread misunderstanding. A forward rate is anchored on spot and the interest-rate differential between the two currencies: a bank can guarantee it without taking a position, by borrowing one currency, converting it and placing the other until maturity. No expectation about the future level of the pair enters that mechanism. The price actually quoted does, however, reflect supply and demand on the FX swap market, which is not the same thing as a forecast.
What are forward points?
They are the gap between the forward rate and the spot rate, expressed in points, that is in the last decimals of the quote. A move from 1.0850 to 1.0955 is 105 points. They are positive at a premium and negative at a discount, depending on the direction of the rate differential. They are instruments in their own right: they trade on the FX swap market, with their own bid and offer.
How do you deduce the bank's margin from the forward rate?
By comparing the rate quoted with the reference forward rate for the same maturity, computed at the same moment. The difference, relative to that reference, gives the order of magnitude of the margin. It is not exactly the margin: the gap also contains the FX swap market's bid-offer and the basis between the two currencies. On a major pair at a common maturity, those two stay small next to the commercial margin; on an illiquid currency or a distant maturity, they no longer do. Comparing the forward rate quoted with today's spot rate, on the other hand, means nothing: that gap is interest rate, not margin.
Why does the forward rate I compute differ from my bank's quote, even without margin?
For three reasons unrelated to its remuneration. First, forward points are quoted on the FX swap market with a bid and an offer: there is one price to buy and another to sell, and you are on the wrong side of both. Second, each currency's actual funding rate differs from the reference rates you looked up. Third, the cross-currency basis means interest-rate parity does not hold exactly, particularly on illiquid currencies, long maturities and across quarter-ends. These gaps stay modest on a major pair at three or six months; they become significant elsewhere.
Is there a free forward rate calculator?
Yes. Our pricer runs this calculation from current market data and shows the gap between the reference rate and the one your bank quoted, as a percentage of notional and in euros. It is free and requires no account.
Why divide by 360 and not 365?
Because most money markets, including the euro and the dollar, count interest on a 360-day basis. Not every currency follows that convention: sterling counts in 365. Using the wrong basis introduces an error that grows with the maturity and can reach the order of magnitude of what you are trying to measure.
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