Exchange Rate Calculations

Economics. Worth 6 to 9 percent of the exam. One session: the lesson, the rules, the method, then the questions.

EconomicsExchange Rate Calculations
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The lesson

The video lesson for this unit is recorded and waiting to be published. Until it is, the rules and the method below carry everything this session needs; watching is a way of hearing it, not the only way of getting it.

The reading

Five to ten minutes on this one unit: what the exam wants, the idea in plain words, then straight into the trap and the practice.

The exam wants you to identify the base and price currency in a quote, calculate a cross rate from two quotes sharing a common currency, calculate a forward rate under covered interest rate parity, and calculate an annualized forward premium or discount. Every question turns on which currency is priced and which one prices it.

Every exchange rate calculation on this module starts with the same question the stem never asks outright: which currency is being priced, and which currency prices it. A quote written X/Y means X units of the first currency buy one unit of the second; Y, the second currency listed, is the base, the single unit being priced, and X is the price currency, the amount needed to buy it. USD/EUR = 1.20 means 1.20 US dollars buys 1 euro, so EUR is the base. Misreading which side is which flips every subsequent calculation, since the base and price roles feed directly into the formulas below.

A cross rate connects two currencies through a shared third one. When two quotes share a common currency in the same position, both written as X/USD, for instance, dividing one quote by the other cancels the shared currency and leaves the rate between the two remaining currencies: EUR/GBP = (EUR/USD) / (GBP/USD). Multiplying the two quotes instead of dividing them, or dividing in the wrong order, gives either an unrelated number or the reciprocal of the rate actually being asked for.

Covered interest rate parity, CIP, prices a forward exchange rate so that no riskless profit exists between borrowing in one currency and investing in the other. The formula places the price currency's interest rate on top: F = S x (1 + r price) / (1 + r base). This produces a result that runs against intuition: the currency paying the higher interest rate trades forward at a discount, not a premium. If a higher-rate currency also strengthened forward, an arbitrageur could borrow the low-rate currency, convert it, invest at the higher rate, and lock in a stronger forward conversion back for a riskless profit; CIP rules that gap out by construction, which is exactly why the higher-rate currency has to weaken forward to compensate.

A forward premium or discount is quoted as a percentage and, on this exam, annualized using a 360-day convention rather than the 365-day convention used elsewhere in the curriculum: [(F - S) / S] x (360 / days in the forward period). Skipping the annualizing step, or using 365 instead of 360, both land close to the correct figure without actually matching it, which is exactly what makes both errors persistent traps rather than obvious mistakes.

Uncovered interest rate parity, UIP, asks a related but different question: what future spot rate would make an investor indifferent between the two currencies without a forward contract locking anything in. Because no arbitrage enforces UIP the way arbitrage enforces CIP, it frequently fails to hold in practice, which is exactly what leaves room for currency carry trades to exist at all.

A triangular arbitrage check across three currencies USD EUR GBP USD/EUR quote USD/GBP quote EUR/GBP cross rate
Three currencies, three quoted rates. Multiply the two legs the long way around the triangle and compare it to the direct cross rate; if they disagree, an arbitrage exists.

Worked in full

The spot USD/EUR exchange rate is 1.1500 (EUR is the base currency). The one-year USD interest rate is 4 percent and the one-year EUR interest rate is 2 percent. Under covered interest rate parity, what is the one-year USD/EUR forward rate, and which currency trades at a forward discount? USD is the price currency here, so its rate goes in the numerator: F = S x (1 + r_price) / (1 + r_base) = 1.1500 x (1.04 / 1.02) = 1.1500 x 1.019608 = 1.1725. The forward rate is higher than spot, meaning more USD is needed to buy one EUR forward than today: USD, the higher-rate currency, trades at a forward discount, exactly as covered interest rate parity requires.

The same problem, one step removed

Same inputs: spot USD/EUR = 1.1500, USD one-year rate 4 percent, EUR one-year rate 2 percent. Set up F = S x (1 + r_price) / (1 + r_base), placing each rate correctly, and finish the calculation yourself.

The trap

Solving covered interest rate parity with the interest rates flipped, base rate on top instead of price rate on the bottom, produces the exam's standard wrong-answer distractor; sanity-check the result by confirming the higher-rate currency comes out at a forward discount, never a premium.

What this unit turns on

Read these before the questions, not after them. Everything here traces to this module's own lesson and to the 2026 outline.

The base currency is the second one in the quote, the one unit being priced

In a quote written X/Y, Y is the base currency, the single unit being priced, and X is the price currency, the amount of it needed to buy one unit of Y. USD/EUR = 1.2000 means 1.20 USD buys 1 EUR; EUR is the base. Misreading which currency is base is the single most common source of a reversed answer on this topic.

Cross rates cancel the shared currency by dividing, never by multiplying

When two quotes share a common currency in the same position, both as X/USD for instance, dividing one by the other cancels USD and leaves the cross rate between the two remaining currencies: EUR/GBP = (EUR/USD) / (GBP/USD). Multiplying the two quotes, or dividing them in the wrong order, produces either an unrelated number or the reciprocal of the rate actually asked for.

Covered interest rate parity places the price currency's rate on top

The exact CIP formula, F = S x (1 + r_price) / (1 + r_base), forces the higher-yielding currency's forward rate to move in the direction that removes any riskless arbitrage: a currency with the higher interest rate trades forward at a discount, and the currency with the lower interest rate trades forward at a premium, so that borrowing in the low-rate currency to invest in the high-rate one, hedged with a forward, earns no free profit.

The higher-interest-rate currency trades forward at a discount, not a premium

This result runs against the carry-trade intuition that a higher rate should make a currency more attractive and push it up. Under CIP the opposite holds by construction: if the high-rate currency also strengthened forward, an arbitrageur could borrow the low-rate currency, convert it, invest at the higher rate, and lock in the stronger forward conversion back, for a riskless profit. CIP is the no-arbitrage condition that rules this out, so the forward move exactly offsets the rate advantage.

A forward premium or discount is annualized on a 360-day convention

The forward premium or discount, expressed as a percentage, is [(F - S) / S] x (360 / days in the forward period), following money-market convention rather than the 365-day convention used elsewhere. Forgetting to annualize, or using 365 instead of 360, both produce an answer close to but not matching the keyed choice.

The trick

The base is the one you are pricing

Read X/Y as X per one Y. Y, the second currency, is always the base, the single unit priced in terms of the first.

Cross rates: divide to cancel, never multiply

Two quotes sharing a common currency in the same slot cancel by division. If both quotes are X/USD, EUR/GBP = (EUR/USD) divided by (GBP/USD).

High rate, forward discount

Under CIP, the currency paying the higher interest rate always trades forward at a discount. A high-rate currency that also traded forward at a premium would hand an arbitrageur a free profit, which CIP rules out by construction.

Annualize on 360, not 365

FX and money-market conventions on this exam use a 360-day year for annualizing a forward premium or discount, a different convention than bond-market day counts elsewhere in the curriculum.

The method

The order to work a question of this type in, every time, before you touch the numbers.

  1. Identify the price currency and the base currency in every quote before doing any arithmetic; write out which one is the one unit being priced.
  2. For a cross rate, confirm both source quotes share a common currency in the same position, then divide to cancel it rather than multiplying.
  3. For a forward rate under covered interest rate parity, place the price currency's interest rate in the numerator and the base currency's rate in the denominator of (1 + r_price)/(1 + r_base), then multiply by spot.
  4. For a premium or discount question, compute (F - S)/S first, then multiply by (360/days) if the question asks for an annualized figure; do not skip the annualizing step.
  5. Sanity-check the direction: the higher-interest-rate currency should come out at a forward discount; if your answer shows it at a premium, recheck which rate went in the numerator.

Two worked examples, then you are on your own

The first is worked in full. The second gives you the setup and stops. After that the questions give you nothing, which is the point: the help fades on purpose, so the last thing you practise is the thing the exam actually asks of you.

Worked in full

The USD/EUR spot exchange rate is 1.1200. A dealer quotes a 90-day forward rate of 1.1050. Which of the following is most accurate?

Answer B. The correct answer is The EUR is at a forward discount relative to the USD.

Your turn, setup given

The spot rate for EUR/USD is 0.8929 (EUR per USD). The spot rate for GBP/USD is 0.7692 (GBP per USD). The EUR/GBP cross rate is closest to:

Identify the price currency and the base currency in every quote before doing any arithmetic; write out which one is the one unit being priced.

The practice run

Pick an answer, say how sure you are, then reveal. Being sure and wrong is the most useful thing that can happen in a session, so answer honestly: it sends the unit back to learning and puts it at the front of your revision queue.

Question 1Exam level

Country A has an annual inflation rate of 6% and Country B has an annual inflation rate of 2%. According to relative purchasing power parity, Country A's currency will most likely:

How sure are you?

Correct: B. The correct answer is Depreciate by approximately 4% per year relative to Country B's currency.
A. Students mix up the direction. They know inflation and exchange rates are related but guess the wrong direction. Higher inflation erodes purchasing power, causing depreciation, not appreciation.
C. Students add both inflation rates: 6% + 2% = 8%. Relative PPP uses the DIFFERENCE in inflation rates (6% - 2% = 4%), not the sum.

Unit: exchange-rate-calculations

Question 2Exam level

The USD/EUR spot rate is 1.2000. The 1-year USD interest rate is 5% and the 1-year EUR interest rate is 3%. According to covered interest rate parity, the 1-year USD/EUR forward rate is closest to:

How sure are you?

Correct: B. The correct answer is 1.2233.
A. You might invert the ratio: 1.2000 × (1.03 / 1.05) = 1.1771. The price currency interest rate goes in the numerator of the CIP formula. USD (price currency in USD/EUR) has the 5% rate. It goes on top.
C. You might use an approximate addition formula: 1.2000 × (1 + 0.05 - 0.03) = 1.2000 × 1.02 = 1.2240. The exact CIP formula uses the ratio (1 + r_price)/(1 + r_base), not a subtraction. The exact answer is 1.2233, not 1.2240.

Unit: exchange-rate-calculations

Question 3Exam level

Which of the following best describes the difference between covered interest rate parity (CIP) and uncovered interest rate parity (UIP)?

How sure are you?

Correct: B. The correct answer is CIP is enforced by arbitrage and uses forward contracts; UIP is an expectation with no arbitrage enforcement.
A. Students confuse the instruments used. CIP uses forward rates (not spot), and UIP relates expected future spot to current spot. CIP uses the forward rate, not just the spot rate. This answer reverses the instruments.
C. Students recall that developed market currency forward markets are more liquid and generalize incorrectly. The CIP vs UIP distinction is about hedging (forward contract) vs expectations, not about market type.

Unit: exchange-rate-calculations

Question 4Harder

A Canadian investor notices that the USD/CAD spot rate is 1.3200. 1-year Canadian interest rate: 4%; 1-year US interest rate: 2%. According to CIP, which of the following is most likely true about the 1-year forward rate?

How sure are you?

Correct: A. Covered interest rate parity: F(USD/CAD) = S(USD/CAD) x (1 + r_CAD) / (1 + r_USD) = 1.3200 x (1.04 / 1.02) = 1.3200 x 1.0196 = 1.3459. The forward rate (CAD per USD) rises above the spot rate, meaning USD buys more CAD forward than it does today: the USD trades at a forward premium to the CAD. The general rule is that the currency with the HIGHER interest rate (CAD, at 4%) trades at a forward discount, and the currency with the LOWER interest rate (USD, at 2%) trades at a forward premium, so that no riskless arbitrage is possible between investing at home versus investing abroad and covering the currency risk forward.
B. This states the opposite of what covered interest rate parity implies here. CAD carries the HIGHER interest rate (4% versus USD's 2%), and the higher-interest currency is the one that trades at a forward DISCOUNT, not a premium; it is the USD, the lower-interest currency, that trades at the forward premium.
C. The forward rate equals the spot rate only when the two currencies' interest rates are identical. Here Canadian and US rates differ (4% versus 2%), so covered interest rate parity requires the forward rate to diverge from spot precisely to offset that interest rate differential; there is no interest-rate-neutral basis for them to stay equal.

Unit: exchange-rate-calculations

Question 5Exam level

The current spot rate for GBP/USD is 1.2500. Inflation in the UK is 4% per year; inflation in the US is 2% per year. According to relative PPP, the expected spot rate in one year is closest to:

How sure are you?

Correct: B. The correct answer is 1.2255.
A. You might put UK inflation in numerator: 1.2500 × (1.04 / 1.02) = 1.2745. They have the ratio backwards. The price currency (USD) inflation goes in the numerator. Base currency (GBP) with higher inflation depreciates. The rate falls.
C. You might use approximate formula: 1.2500 × (1 - 0.02) = 1.2250. Subtracting the inflation differential directly. The approximate answer is close but the question asks for 'closest to'. Need to apply the exact formula for precision.

Unit: exchange-rate-calculations

Question 6Exam level

If the Japanese yen depreciates significantly against the USD, which of the following is the most likely effect on Japan's trade balance?

How sure are you?

Correct: B. The correct answer is Japan's trade balance will improve as exports become cheaper to foreign buyers and imports become more expensive.
A. You might confuse direction. 'depreciation' sounds negative so they assign negative trade effects. Depreciation makes EXPORTS cheaper (not imports). Imports become MORE expensive, not cheaper, in the depreciating currency.
C. You might recall the long-run PPP argument that exchange rates adjust to equalize prices and extrapolate incorrectly. PPP describes long-run equilibration, not an invariance of trade effects. Currency depreciation does affect trade balances, especially in the short-to-medium run.

Unit: exchange-rate-calculations

Question 7Exam level

An exchange rate is quoted as CAD/USD = 1.3500. This quote is most likely described as:

How sure are you?

Correct: A. The correct answer is A direct quote for a Canadian investor.
B. Students confuse the definition: they think 'more units = indirect' or they flip the domestic/foreign assignment. Direct quote = domestic currency per unit of foreign. CAD/USD for a Canadian is domestic (CAD) per foreign (USD) = direct quote.
C. Students see USD in the quote and assume it must be a direct quote 'for' the USD side. For a US investor, CAD/USD means foreign (CAD) per domestic (USD). That is an INDIRECT quote for the US investor.

Unit: exchange-rate-calculations

Question 8Exam level

Spot USD/EUR = 1.1000. 90-day forward USD/EUR = 1.1200. The annualized forward premium on the EUR is closest to:

How sure are you?

Correct: B. The correct answer is 7.27%.
A. You might calculate (0.0200 / 1.1000) = 1.82% but forget to annualize by multiplying by (360/90) = 4. The question asks for the ANNUALIZED forward premium. Must multiply by (360/days).
C. You might calculate (0.0200 / 1.1100) × 4 using the average of spot and forward, or use 1.80% as (0.02/1.1) × 4 rounding. The denominator is the spot rate (1.1000), not the midpoint or forward rate. Precise calculation gives 7.2727%, which rounds to 7.27%.

Unit: exchange-rate-calculations

Question 9Exam level

According to absolute purchasing power parity, the exchange rate between two currencies equals, most likely:

How sure are you?

Correct: B. The correct answer is The ratio of price levels in the two countries.
A. You might confuse PPP with interest rate parity. Both are parity conditions, and the interest rate connection is salient. Interest rate ratio is the basis for interest rate parity (CIP/UIP), not PPP. PPP is about price levels, not interest rates.
C. This describes RELATIVE PPP, not absolute PPP. Both PPP variants involve exchange rates and inflation. Relative PPP describes the expected CHANGE in exchange rates based on inflation differentials. Absolute PPP describes the exchange rate LEVEL based on price ratios.

Unit: exchange-rate-calculations

Question 10Harder

Under uncovered interest rate parity, if the domestic interest rate is higher than the foreign interest rate, the domestic currency is most likely expected to:

How sure are you?

Correct: B. The correct answer is Depreciate by the interest rate differential.
A. Students think higher interest rates mean more capital inflows, which should strengthen the currency. UIP says higher rates come with expected depreciation to prevent a free profit from interest differentials. The expected depreciation offsets the rate advantage.
C. Students recall that arbitrage enforces CIP and incorrectly apply this to UIP. Arbitrage enforces CIP (via forward contracts). UIP is not enforced by arbitrage. It is an expectation that requires taking currency risk.

Unit: exchange-rate-calculations

Question 11Above the exam

The current spot rate is USD/EUR 1.10 (1.10 USD per EUR). The 1-year USD interest rate is 5% and the 1-year EUR interest rate is 2%. An investor believes covered interest rate parity should hold, but the actual 1-year forward rate quoted in the market is USD/EUR 1.15. Combining the no-arbitrage forward rate with the quoted market rate, the situation most likely presents:

How sure are you?

Correct: B. Covered interest rate parity implies the no-arbitrage forward rate = spot x (1 + USD rate)/(1 + EUR rate) = 1.10 x 1.05/1.02 = 1.10 x 1.0294 = 1.1324. The market's quoted forward of 1.15 is higher than this no-arbitrage rate, meaning EUR is priced too expensive forward relative to what the interest rate differential justifies; this mismatch is exactly the signal of a covered interest arbitrage opportunity (borrow in one currency, invest in the other, lock in the forward, and profit risklessly) rather than a situation where parity already holds.
A. Forward rates are not automatically guaranteed to equal the no-arbitrage rate at every moment; real-world forward quotes can and do drift away from the interest-rate-parity value, which is precisely the condition that creates a covered interest arbitrage opportunity when it happens.
C. Covered interest arbitrage is a combined spot-and-forward strategy (borrowing/investing at spot, locking in the exchange back at the forward rate); the mispricing described here is specifically a forward-rate mispricing relative to the interest rate differential, not an isolated spot-market-only issue.

Unit: exchange-rate-calculations

Question 12Above the exam

A US-based investor holds a bond denominated in a foreign currency that returns 8% in local-currency terms over the year. Over the same year, the foreign currency depreciates against the US dollar by 6%. Combining the local-currency return with the currency effect, the investor's approximate total return in USD terms is closest to:

How sure are you?

Correct: B. The approximate total return in the investor's home currency combines the local-market return with the currency return: total return (approx.) = local return + currency return = 8% + (-6%) = 2%. A depreciating foreign currency subtracts from the local-asset return once translated back to US dollars, since each unit of foreign currency (and the gains earned in it) is now worth fewer dollars.
A. 14% adds the local return and the currency change as though the currency also APPRECIATED (8% + 6%), reversing the sign of a depreciation; a depreciating foreign currency should be subtracted from, not added to, the local-currency return.
C. 8% is only the local-currency return, ignoring the currency translation effect entirely. Whenever an asset is held in a foreign currency, the investor's home-currency return depends on both the asset's local performance AND how that currency moved against the home currency.

Unit: exchange-rate-calculations