Lesson 4 of 4 6–9% of the exam

By Daniil Tarakanov Updated Oct 21, 20262027 curriculum

Currency forward prices and the interest rate differential

Q: How do you calculate a currency forward rate?

Multiply the spot rate by e^((r_f − r_d)T), where r_f is the risk-free rate of the price currency (the numerator of the quote), r_d is the rate of the base currency and T is in years. With discrete compounding, multiply by ((1 + r_f) ÷ (1 + r_d))^T.

Q: Why does the higher interest rate currency trade at a forward discount?

Holding the higher-rate currency earns more interest, so the forward must give up value to leave no arbitrage. A trader who borrows the low-rate currency and lends the high-rate one earns the extra interest, but loses exactly that much converting back at the weaker forward rate.

Q: What is the base currency in an exchange rate quote?

In a quote S f/d the base currency d is the denominator: one unit of it costs S units of the price currency f. A USD/EUR rate of 1.08 means USD 1.08 per EUR 1, so the euro is the base currency.

Holding a currency earns its own risk-free rate, so a currency forward is priced by carry like any asset: F = S × e^((r_f − r_d)T), with f the price currency and d the base currency. The currency with the higher interest rate trades at a forward discount.

6 min cram, 28 min full read. Based on the 2027 CFA® Program Level I curriculum, Derivatives, Learning Module 4. Also part of the 2026 curriculum, so it applies to the November 2026 exam too.

Tailor this to you: take the self-assessment

Before this: Cost of carry: income, storage and convenience yield, Exchange Rate Calculations

On the exam

Explain the difference between the spot and expected future price of an underlying and the cost of carry associated with holding the underlying asset

Explain the carry relationship for currencies. Expect a forward rate computed from spot and two interest rates, and a call on which currency trades at a forward premium or discount.

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

How is an exchange rate quoted?

An FX forward , where FX means foreign exchange, is an agreement to exchange two currencies at a fixed rate on a future date. To price one you need to read the quote correctly.

A quote S f/d gives the number of units of the price currency (f, the numerator) needed to buy one unit of the base currency (d, the denominator). JPY/USD 150.00 means JPY 150 for USD 1, so the yen is the price currency and the dollar is the base currency.

Reading an exchange-rate quote S f/d

Quote S f/dunits of f per one unit of d

Price currency, f Memorize the numerator; carries the rate r_f (the "foreign" rate)
Base currency, d Memorize the denominator, one unit; carries the rate r_d (the "domestic" rate)
Long FX forward Memorize a foreign exchange (FX) forward: buy the base currency, sell the price currency

Each currency can be lent or borrowed at its own risk-free rate. The curriculum calls the price currency’s rate the foreign risk-free rate , r_f, and the base currency’s rate the domestic risk-free rate , r_d. The labels follow the letters f and d. They do not tell you where the investor lives.

What is the currency forward price?

A currency is an asset that pays interest, so the carry logic applies. Holding the base currency earns r_d. Holding the price currency earns r_f. The no-arbitrage forward rate is the spot rate grown by the difference between the two. The curriculum uses continuous compounding here.

Currency forward rate Memorize

F_{0,f/d}(T) = S_{0,f/d}\,e^{(r_f - r_d)T}

Rearrange itCurrency forward rate: solve for any input

The question asks for

The spot rate is 150 units of the price currency per unit of the base currency. The continuously compounded rate is 0.50% in the price currency and 4.50% in the base currency. The no-arbitrage forward rate for 1 years ahead is closest to:

Spot rate, S₀ (price currency per base)Price-currency rate, r_f (continuous)%Base-currency rate, r_d (continuous)%Time to expiration, T (years)

F_{0, f / d} (T) = S_{0, f / d} e^{(r_{f} - r_{d}) T}

150 × e^((0.005 − 0.045) × 1) = 144.1184

Forward rate, F₀(T) (price currency per base)144.1184

On your calculator

0.005−0.045=×1=-0.04
2NDe^x×150=144.1184

2ND second function (the shifted label above a key) · e^x e to the power x

0.005ENTER0.045−1×-0.04
ge^x150×144.1184

ENTER enter (on the HP, puts the number on the stack) · g blue shift key · e^x e to the power x

Why that number? Replicate the forward on USD 1,000, using the price-currency and base-currency loans:

Borrow USD 1,000 at 4.5%. In one year you owe 1,000 × e^0.045 = USD 1,046.03.
Convert at spot into JPY 150,000 and lend it at 0.5%. In one year you receive 150,000 × e^0.005 = JPY 150,751.88.
Locking in the rate: the JPY 150,751.88 exactly repays the USD 1,046.03 debt if USD 1 is exchanged at 150,751.88 ÷ 1,046.03 = JPY 144.12.

Any other forward rate would leave a riskless profit for one side. This is the same borrow, buy, lend argument as before, with a second interest rate.

InteractivePrice a currency forward by carry

Try this 0 of 3

Switch to discrete compounding and compare the forward
Raise the JPY rate above the USD rate and see which currency moves to a premium
Shorten the term to 6 months

Spot JPY/USD (JPY per USD)

JPY rate (price currency)0.50%

USD rate (base currency)4.50%

Term

Compounding

Parity forward JPY/USD144.12

F − S−5.88

Forward premiumJPY +4.081%

Forward discountUSD −3.921%

USD at a forward discount (USD pays the higher rate, 4.50% vs 0.50%).

Replicate the forward with USD 1,000

BorrowUSD 1,000.00 at 4.50%owe USD 1,046.03
Convertat spot 150.00JPY 150,000.00
LendJPY at 0.50%JPY 150,751.88
Locksell JPY forward at 144.12USD 1,046.03
Netrepay USD 1,046.03USD 0.00

Show working

F(JPY/USD) = S × e^(rT) for JPY ÷ the same for USD: the price currency's rate on top, the base currency's below.

F = 150.00 × e^(0.0050 × 1.0000) ÷ e^(0.0450 × 1.0000) = 150.00 × 1.005013 ÷ 1.046028 = 144.12

F − S = 144.12 − 150.00 = −5.88

USD (base) discount: F ÷ S − 1 = −3.921%

Traps: swapping the rates gives 156.12.

Same inputs, other compounding: discrete 144.26.

The forward on your calculator

0.005−0.045=2NDe^x×150=144.12, the forward
−150=−5.88, f − s

2ND second function (the shifted label above a key) · e^x e to the power x

0.005ENTER0.045−ge^x150×144.12, the forward
150−−5.88, f − s

ENTER enter (on the HP, puts the number on the stack) · g blue shift key · e^x e to the power x

The forward rate moves by the interest rate gap, not by anyone's view of the currency.

For discrete compounding, which Economics uses for covered interest rate parity, the same logic gives a ratio of growth factors.

Currency forward rate, discrete compounding Use it

F_{0,f/d}(T) = S_{0,f/d}\left(\frac{1 + r_f}{1 + r_d}\right)^T

With the yen-dollar numbers, the discrete version is 150 × 1.005 ÷ 1.045 = 144.26, close to the continuous 144.12.

Which currency trades at a forward premium?

Forward premium and forward discount describe a currency whose forward price is above or below its spot price, in terms of the other currency. Use the sign of r_f − r_d.

Which currency trades at a forward premium

Compare the two interest rates, r_f − r_dthe rate gap sets the forward, not the level of either rate

r_f above r_d Memorize F₀ above S₀
- Price currency f forward discount (higher rate)
- Base currency d forward premium
r_f below r_d Memorize F₀ below S₀
- Price currency f forward premium
- Base currency d forward discount (higher rate)
r_f equals r_d F₀ equals S₀; neither premium nor discount

Think of it as the rate gap being paid back through the exchange rate. The higher-rate currency pays more interest, so it must buy fewer units of the other currency forward than at spot. That is a forward discount.

Worked example A case where the base currency is the high-rate one

The USD/GBP spot rate is 1.2500 (USD per GBP). The USD risk-free rate is 3.5% and the GBP rate is 5.5% (continuous). What is the six-month forward rate and which currency is at a discount?

The quote is USD per GBP, so USD is the price currency (f) and GBP is the base currency (d).
F = 1.2500 × e^((0.035 − 0.055) × 0.5) = 1.2376.
F is below S. The GBP, with the higher rate, is at a forward discount. The USD is at a forward premium.

On your calculator

0.035−0.055=×0.5= -0.01
2NDe^x×1.25= 1.2376

2ND second function (the shifted label above a key) · e^x e to the power x

0.035ENTER0.055−0.5× -0.01
ge^x1.25× 1.2376

ENTER enter (on the HP, puts the number on the stack) · g blue shift key · e^x e to the power x

Exam tip Name the price currency first. Its rate goes first in the exponent. Then: higher rate, forward discount.

Go deeper Covered interest rate parity in Economics

The Economics module on exchange rates derives the same result as covered interest rate parity, with discrete rates. The forward rate equals the spot rate adjusted by the interest rate gap, which removes any riskless profit from borrowing in one currency and lending in the other. Same idea, different compounding convention. The two answers differ slightly (144.12 against 144.26 in the yen-dollar example), so use the convention the question states.

Go deeper Is the forward rate a forecast of the future spot rate?

No. The forward rate comes from the interest rate gap alone. The currency with the high rate trades at a forward discount, yet it does not follow that it will depreciate. The forward rate is not a prediction of the future spot rate, just as an asset’s forward price is not its expected future price.

Memorize this

MemorizeThe currency forward

$r_f - r_d$	Forward against spot	Price currency $f$	Base currency $d$
> 0	$F > S$	discount	premium
< 0	$F < S$	premium	discount
= 0	$F = S$	neither	neither

Memory hook Higher interest rate means a weaker forward: that currency trades at a discount. Price-currency rate goes on top of the exponent.

Know it cold $F_{f/d} = S_{f/d}\,e^{(r_f - r_d)T}$ . $f$ = price currency (numerator), $d$ = base currency (denominator). A long FX forward buys the base currency.

Reading an exchange-rate quote S f/d

Quote S f/dunits of f per one unit of d

Price currency, f Memorize the numerator; carries the rate r_f (the "foreign" rate)
Base currency, d Memorize the denominator, one unit; carries the rate r_d (the "domestic" rate)
Long FX forward Memorize a foreign exchange (FX) forward: buy the base currency, sell the price currency

Which currency trades at a forward premium

Compare the two interest rates, r_f − r_dthe rate gap sets the forward, not the level of either rate

r_f above r_d Memorize F₀ above S₀
- Price currency f forward discount (higher rate)
- Base currency d forward premium
r_f below r_d Memorize F₀ below S₀
- Price currency f forward premium
- Base currency d forward discount (higher rate)
r_f equals r_d F₀ equals S₀; neither premium nor discount

Currency forward rate

F_{0,f/d}(T) = S_{0,f/d}\,e^{(r_f - r_d)T}

Quick example

NOK/GBP spot 13.20 (NOK per GBP), NOK rate 2.5%, GBP rate 4.5%, three months (continuous). 13.20 × e^((0.025 − 0.045) × 0.25) = 13.134. The higher-rate GBP trades at a forward discount.

On your calculator

0.025−0.045=×0.25=2NDe^x×13.2= 13.1342

2ND second function (the shifted label above a key) · e^x e to the power x

0.025ENTER0.045−0.25×ge^x13.2× 13.1342

ENTER enter (on the HP, puts the number on the stack) · g blue shift key · e^x e to the power x

Currency forward rate, discrete compounding

F_{0,f/d}(T) = S_{0,f/d}\left(\dfrac{1 + r_f}{1 + r_d}\right)^T

Quick example

SEK/USD spot 10.50, SEK rate 3%, USD rate 5%, six months. 10.50 × (1.03 ÷ 1.05)^0.5 = 10.40.

On your calculator

1.03÷1.05=y^x0.5=×10.5= 10.3995

y^x power

1.03ENTER1.05÷0.5y^x10.5× 10.3995

ENTER enter (on the HP, puts the number on the stack) · y^x power

How it is asked

Compute the forward rate

PLN/EUR 4.50, PLN rate 6%, EUR rate 2%, six months (continuous).

4.50 × e^(0.04 × 0.5) = 4.59. Traps: 4.41 (rates reversed), 4.50 (no differential).
Premium or discount

Price-currency rate below base-currency rate. Base currency at a forward premium or discount?

r_f − r_d < 0, so F < S: the base currency is at a discount. Trap: calling the higher-rate currency the premium one.
What does a long forward do

Long position in a USD/GBP forward.

Buys the base currency: buy GBP, sell USD. Trap: reading the quote backwards.

Exam traps

Reversing r_f and r_d. The price currency's rate goes on top of the exponent: (r_f − r_d), with f the numerator of the quote.
Calling the higher-rate currency the one at a premium. The higher-rate currency trades at a forward discount.
Mixing up the price and base currencies in a quote. In S f/d, one unit of d costs S units of f.
Using the rate levels instead of their difference. Only r_f − r_d matters.

Checkpoint

5 exam-style questions. About 90 seconds each.

1The MXN/EUR spot rate is 20.00 (MXN per EUR). The MXN risk-free rate is 9% and the EUR rate is 3% (both continuously compounded). The six-month forward rate is closest to:
2If the price currency's interest rate is below the base currency's, the base currency trades at a forward:
3A long position in a USD/GBP forward (USD per GBP) commits the holder to:
4The CHF/EUR spot rate is 0.9500 (CHF per EUR). The CHF risk-free rate is 1.0% and the EUR rate is 3.0% (both continuously compounded). The one-year forward rate is closest to:
5In the AUD/USD quote (AUD per USD), the AUD risk-free rate is 4.0% and the USD rate is 5.0%. The AUD trades at a forward:

Key takeaways

F = S × e^((r_f − r_d)T), with f the price currency and d the base currency.
The higher-rate currency trades at a forward discount; the lower-rate currency at a premium.
A long FX forward buys the base currency forward.
The forward rate depends on the interest rate gap, not on anyone's view of the currency.

Currency forward rate

F_{0,f/d}(T) = S_{0,f/d}\,e^{(r_f - r_d)T}

Quick example

NOK/GBP spot 13.20 (NOK per GBP), NOK rate 2.5%, GBP rate 4.5%, three months (continuous). 13.20 × e^((0.025 − 0.045) × 0.25) = 13.134. The higher-rate GBP trades at a forward discount.

On your calculator

0.025−0.045=×0.25=2NDe^x×13.2= 13.1342

2ND second function (the shifted label above a key) · e^x e to the power x

0.025ENTER0.045−0.25×ge^x13.2× 13.1342

ENTER enter (on the HP, puts the number on the stack) · g blue shift key · e^x e to the power x

Currency forward rate, discrete compounding

F_{0,f/d}(T) = S_{0,f/d}\left(\dfrac{1 + r_f}{1 + r_d}\right)^T

Quick example

SEK/USD spot 10.50, SEK rate 3%, USD rate 5%, six months. 10.50 × (1.03 ÷ 1.05)^0.5 = 10.40.

On your calculator

1.03÷1.05=y^x0.5=×10.5= 10.3995

y^x power

1.03ENTER1.05÷0.5y^x10.5× 10.3995

ENTER enter (on the HP, puts the number on the stack) · y^x power

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Next module: Pricing and Valuing Forward Contracts and FRAs Forward price vs forward value: at initiation, during the life, at expiry

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Where this comes back

Pricing and Valuing Forward Contracts and FRAs Derivatives
Exchange Rate Calculations Economics

Questions candidates ask

How do you calculate a currency forward rate?

Multiply the spot rate by e^((r_f − r_d)T), where r_f is the risk-free rate of the price currency (the numerator of the quote), r_d is the rate of the base currency and T is in years. With discrete compounding, multiply by ((1 + r_f) ÷ (1 + r_d))^T.

Why does the higher interest rate currency trade at a forward discount?

Holding the higher-rate currency earns more interest, so the forward must give up value to leave no arbitrage. A trader who borrows the low-rate currency and lends the high-rate one earns the extra interest, but loses exactly that much converting back at the weaker forward rate.

What is the base currency in an exchange rate quote?

In a quote S f/d the base currency d is the denominator: one unit of it costs S units of the price currency f. A USD/EUR rate of 1.08 means USD 1.08 per EUR 1, so the euro is the base currency.

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