Practice: Exchange Rate Calculations

Economics. 14 question(s) in this unit's pool (2 above the exam). Free up to ten a day; the coach picks which ones based on what you have already answered and when each is next due.

EconomicsExchange Rate Calculations
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Today's practice

Pick an answer, say how sure you are, then reveal. Every wrong choice gets its own explanation. Questions you have already answered correctly and confidently stay out of the way until they are due for review again.

Question 1Exam level

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?

How sure are you?

Correct: B. The correct answer is The EUR is at a forward discount relative to the USD.
A. You might see a lower forward rate and think 'fewer units = stronger' for the base currency (USD), but in USD/EUR notation, the USD is the price currency, not base. In USD/EUR, EUR is the base. EUR buys fewer USD forward than spot, so EUR is at a discount, not USD.
C. You might confuse which direction means premium. Some think 'lower number = premium for the price currency'. A currency is at a forward premium when it buys MORE of the other currency forward vs spot. EUR buys fewer USD forward, so EUR is at a discount.

Unit: exchange-rate-calculations

Question 2Exam level

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:

How sure are you?

Correct: A. The correct answer is 1.1607.
B. You might multiply instead of divide: 0.8929 × 0.7692 ≈ 0.6868, or divide in reverse. To eliminate USD from both quotes, you divide the EUR/USD rate by the GBP/USD rate.
C. Inverts the calculation. Uses GBP/EUR instead of EUR/GBP. This gives GBP/EUR = 0.7692 / 0.8929 = 0.8613, which is the reciprocal of the asked cross rate.

Unit: exchange-rate-calculations

Question 3Exam 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 4Exam 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 5Exam 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 6Harder

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 7Exam 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 8Exam 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 9Exam 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 10Exam 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 11Exam 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 12Harder

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 13Above 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 14Above 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