FIN415 Final Exam Study Guide
Calculation Practice

This page focuses on the 70-point calculation part. Each worked example now starts with the math equation first, then explains what each symbol means, then shows a slow step-by-step solution. Where a matching JUFinance tool or calculator is available, the guide points you there too.

How to study 1–3 4–6 7–9 10–12 13–15
Theme

How to use this page

Step 1 — Say what the question is asking

Before touching the numbers, decide whether the problem is asking for an expected FX rate, a hedge cost, an arbitrage profit, an option payoff/profit, or an effective borrowing cost after a swap.

Step 2 — Match the equation to the story

If the story is about inflation, use PPP. If it is about interest rates and expected FX, use IFE. If it is about spot, forward, and interest rates, use IRP. If it is about payoffs, separate payoff from profit.

Step 3 — Keep the quote direction straight

A lot of mistakes happen because students know the formula but flip the quote. Always say what one unit of the base currency costs in the quoted currency.

Good exam habit: write the equation first, label the symbols, substitute carefully, then interpret the answer in words. A final number without interpretation is often where students lose easy points.
Memory help for options: CALL = UP and PUT = DOWN. A call helps when the foreign currency may go up in price. A put helps when the foreign currency may go down in price.

Problem 1 — Module 8: Relative PPP

Find the expected future spot rate using inflation rates.

Relative PPP: E[S1] = S0 × (1 + πhome) / (1 + πforeign)
Suppose the spot rate is 1.60 USD/GBP. U.S. inflation is 9% and U.K. inflation is 5%. Find the expected one-year spot rate.

What the equation means

  • E[S1] = expected future spot rate one period from now
  • S0 = today’s spot rate
  • π_home = inflation rate in the quoted-currency country
  • π_foreign = inflation rate in the base-currency country

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the Module 8 page for the Relative PPP calculator and the worked PPP examples, or open the PPP calculator for quick PPP-style practice.
Show detailed solution
  1. The quote is USD/GBP, so the pound is the base currency and the dollar is the quoted currency.
  2. Because the U.S. is on the quoted-currency side, use U.S. inflation for π_home = 0.09.
  3. Because the U.K. is on the base-currency side, use U.K. inflation for π_foreign = 0.05.
  4. Substitute into the formula: E[S1] = 1.60 × (1.09 / 1.05).
  5. Compute the ratio first: 1.09 / 1.05 = 1.038095.
  6. Now multiply by today’s spot rate: 1.60 × 1.038095 ≈ 1.6610.
Answer: 1.6610 USD/GBP. Because the quote rises from 1.60 to about 1.6610, the pound appreciates versus the dollar and the dollar depreciates.

Problem 2 — Module 8: IFE

Find expected FX using nominal interest rates instead of inflation.

IFE: E[S1] = S0 × (1 + ihome) / (1 + iforeign)
Suppose the spot rate is 1.60 USD/GBP. U.S. nominal interest rate is 8% and U.K. nominal interest rate is 4%. Find the expected one-year spot rate under IFE.

What the equation means

  • E[S1] = expected future spot rate
  • S0 = today’s spot rate
  • i_home = nominal interest rate in the quoted-currency country
  • i_foreign = nominal interest rate in the base-currency country

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: On the Module 8 page, use the IFE calculator that shows the formula substitution step by step.
Show detailed solution
  1. Again, the quote is USD/GBP, so the U.S. is the quoted-currency side and the U.K. is the base-currency side.
  2. Use i_home = 0.08 and i_foreign = 0.04.
  3. Substitute: E[S1] = 1.60 × (1.08 / 1.04).
  4. Compute the ratio first: 1.08 / 1.04 = 1.038462.
  5. Multiply by 1.60: 1.60 × 1.038462 ≈ 1.6615.
Answer: 1.6615 USD/GBP. The interpretation is similar to PPP: the quote rises, so the pound is expected to strengthen relative to the dollar.

Problem 3 — Module 8: Big Mac / Law of One Price style question

Find implied PPP FX and compare it with market FX.

Implied FX (USD per 1 FCY) = Price in U.S. dollars / Price in foreign currency
A Big Mac costs $6.00 in the U.S. and 30 BRL in Brazil. The market exchange rate is 0.18 USD/BRL. Find the implied PPP exchange rate and say whether BRL looks overvalued or undervalued versus the dollar.

What the equation means

  • Implied FX = PPP-style exchange rate implied by the price comparison
  • Price in U.S. dollars = price of the same product in the U.S.
  • Price in foreign currency = price of the same product in the foreign country
  • Market FX = actual exchange rate observed in the market

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the Big Mac / PPP practice area on the Module 8 page or the PPP calculator for quick implied-rate checks.
Show detailed solution
  1. Use the price-ratio idea: implied FX = 6.00 / 30 = 0.20 USD/BRL.
  2. Now compare the implied PPP FX with the market FX.
  3. PPP says 1 BRL should be worth about $0.20, but the market says 1 BRL is only worth $0.18.
  4. That means the real gives fewer dollars in the market than the PPP benchmark suggests.
Answer: PPP-implied FX = 0.20 USD/BRL. Compared with the market rate of 0.18, the BRL looks undervalued relative to the dollar.

Problem 4 — Module 9: Forward hedge cost

Lock in the dollar cost of a euro payment.

Forward cost = Foreign amount × Forward rate
A U.S. payer knows it will need €25,000 in 90 days. The forward rate is 1.0854 USD/EUR. What is the dollar cost if the payer hedges with the forward?

What the equation means

  • Foreign amount = how many units of foreign currency you must pay later
  • Forward rate = exchange rate locked in today for future settlement
  • Forward cost = certain dollar amount you lock in today

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the Module 9 page or the JU IRP calculator to check the forward rate and hedge cost.
Show detailed solution
  1. This is the simplest kind of forward-hedge question: amount × forward rate.
  2. The quote is USD/EUR, so each euro costs $1.0854.
  3. Multiply the number of euros needed by the dollar cost per euro: 25,000 × 1.0854.
  4. That gives 27,135.
Answer: $27,135. The main idea is that the firm removes uncertainty by fixing the future dollar cost today.

Problem 5 — Module 9: Long futures payoff

Use the long-futures payoff formula.

Long futures payoff = Contract size × (Spot at maturity − Settlement price)
A trader opens a long pound futures position. Contract size is £62,500. Settlement price is $1.40/£. At maturity, spot is $1.50/£. Find the payoff.

What the equation means

  • Contract size = how many units of the underlying are covered by the futures contract
  • Spot at maturity = actual market price when the contract ends
  • Settlement price = price fixed in the futures contract
  • Long futures payoff = gain or loss for the long position

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the JU futures payoff calculator or the Module 9 page for futures P&L practice.
Show detailed solution
  1. A long futures position wins when the final spot price is above the settlement price.
  2. Compute the price change first: 1.50 − 1.40 = 0.10 dollars per pound.
  3. Now multiply by the contract size: 62,500 × 0.10.
  4. That gives 6,250.
Answer: +$6,250. The price went up, so the long side gains.

Problem 6 — Module 9: Short futures payoff

Use the short-futures payoff formula.

Short futures payoff = − Contract size × (Spot at maturity − Settlement price)
A trader opens a short pound futures position. Contract size is £62,500. Settlement price is $1.60/£. At maturity, spot is $1.50/£. Find the payoff.

What the equation means

  • Negative sign = reminds you that short is the opposite side of long
  • Contract size = number of underlying units
  • Spot at maturity = actual final market price
  • Settlement price = contract price locked in at the start

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the JU futures payoff calculator to compare long and short payoff signs quickly.
Show detailed solution
  1. A short futures position wins when the final spot price is below the settlement price.
  2. Compute the price change first: 1.50 − 1.60 = −0.10.
  3. Now apply the short formula: −62,500 × (−0.10).
  4. A negative times a negative becomes a positive.
  5. So the payoff is +6,250.
Answer: +$6,250. The price fell, so the short side gains.

Problem 7 — Module 11: Solve the forward rate from IRP

Use spot, rates, and time to find the fair forward.

IRP: F = S × (1 + iq × T) / (1 + ib × T)
Spot is 1.0800 USD/EUR. U.S. annual interest rate is 4.5%, euro annual interest rate is 2.5%, and the horizon is 90/360 years. Find the 90-day forward rate.

What the equation means

  • F = forward rate
  • S = spot rate today
  • i_q = interest rate in the quoted currency
  • i_b = interest rate in the base currency
  • T = time in years, often days/360

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the JUFinance IRP calculator or the Module 11 page for IRP drills.
Show detailed solution
  1. The quote is USD/EUR, so USD is the quoted currency and EUR is the base currency.
  2. That means i_q = 0.045 and i_b = 0.025.
  3. The time fraction is T = 90/360 = 0.25.
  4. Substitute into the equation: F = 1.0800 × (1 + 0.045 × 0.25) / (1 + 0.025 × 0.25).
  5. Compute the numerator: 1 + 0.045 × 0.25 = 1.01125.
  6. Compute the denominator: 1 + 0.025 × 0.25 = 1.00625.
  7. Divide first: 1.01125 / 1.00625 ≈ 1.0049689.
  8. Multiply by 1.0800: F ≈ 1.0854.
Answer: 1.0854 USD/EUR. Because the quoted-currency interest rate is higher, the forward comes out slightly above spot.

Problem 8 — Module 11: Solve the spot rate from IRP

Rearrange the IRP formula correctly.

From F = S × (1 + iq) / (1 + ib), solve for S: S = F × (1 + ib) / (1 + iq)
The one-year U.S. interest rate is 6%, the one-year euro interest rate is 4%, and the one-year forward rate is 1.24 USD/EUR. Find the current spot rate.

What the equation means

  • S = the spot rate you are trying to solve for
  • F = the known forward rate
  • i_b = base-currency interest rate
  • i_q = quoted-currency interest rate

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: The JUFinance IRP calculator can also solve a missing spot from the known forward.
Show detailed solution
  1. The quote is USD/EUR, so EUR is the base currency and USD is the quoted currency.
  2. Therefore i_b = 0.04 and i_q = 0.06.
  3. Use the rearranged equation: S = 1.24 × 1.04 / 1.06.
  4. Multiply first: 1.24 × 1.04 = 1.2896.
  5. Now divide by 1.06: 1.2896 / 1.06 ≈ 1.2166.
Answer: 1.2166 USD/EUR. This is the spot rate consistent with the given forward and interest rates.

Problem 9 — Module 11: Covered interest arbitrage profit idea

Compare the market forward with the no-arbitrage forward.

First compute F* = S × (1 + iq) / (1 + ib), then compare F* with actual F
Suppose S0 = 1.45 USD/EUR, F360 = 1.42 USD/EUR, U.S. rate is 2%, euro rate is 3%, and the contract size is €10,000. Find the no-arbitrage forward first, then estimate the profit at maturity if you can lock in the mispricing.

What the equation means

  • F* = fair no-arbitrage forward rate
  • Actual F = market forward rate being offered
  • Mispricing = difference between fair forward and actual forward
  • Contract size = foreign-currency amount used to estimate profit

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the JUFinance IRP calculator to see whether the market forward is above or below parity.
Show detailed solution
  1. The quote is USD/EUR, so USD is the quoted currency and EUR is the base currency.
  2. That means i_q = 0.02 and i_b = 0.03.
  3. Compute the fair forward: F* = 1.45 × 1.02 / 1.03 ≈ 1.4359 USD/EUR.
  4. Compare the market forward with the fair forward: actual F = 1.42 is below the fair 1.4359.
  5. So the market forward is too low relative to parity.
  6. A quick maturity-value estimate of the locked spread on €10,000 is (1.4359 − 1.42) × 10,000.
  7. That gives about 0.0159 × 10,000 = $159.
Approximate locked-in profit at maturity: $159 on the €10,000 amount. On an exam, also explain that the exact arbitrage uses borrow–convert–invest–hedge steps.

Problem 10 — Module 12: Locational arbitrage

Use ask to buy and bid to sell.

Profit per unit = Higher bid − Lower ask
Bank 1 quotes pounds at bid 1.60, ask 1.61 USD/£. Bank 2 quotes pounds at bid 1.62, ask 1.63 USD/£. Start with $1,610. Show the arbitrage profit.

What the equation means

  • Ask = price you pay to buy the foreign currency from the dealer
  • Bid = price the dealer pays when you sell the foreign currency back
  • Higher bid = better selling price
  • Lower ask = better buying price

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the locational arbitrage calculator on the Module 12 page for the same dealer-comparison logic.
Show detailed solution
  1. Start by asking: where is it cheaper to buy pounds? Answer: Bank 1, because its ask is 1.61, which is lower than Bank 2’s ask of 1.63.
  2. Buy pounds at Bank 1 ask: $1,610 / 1.61 = £1,000.
  3. Now ask: where is it better to sell pounds? Answer: Bank 2, because its bid is 1.62, which is higher than Bank 1’s bid of 1.60.
  4. Sell the £1,000 at Bank 2 bid: £1,000 × 1.62 = $1,620.
  5. Compare ending dollars with starting dollars: $1,620 − $1,610 = $10.
Answer: $10 profit. The key memory rule is: buy at the ask, sell at the bid.

Problem 11 — Module 12: Triangular arbitrage

Test the full currency loop carefully.

For a USD → GBP → MYR → USD loop: Ending USD = Starting USD ÷ (USD/GBP quote) × (MYR per GBP) × (USD per MYR)
Given: £ = $1.50, MYR = $0.25, and the cross rate is £1 = MYR 6.1. Start with $1,500. Is there triangular arbitrage?

What the equation means

  • Starting USD = the dollar amount you begin with
  • USD/GBP quote = dollars needed to buy 1 pound
  • MYR per GBP = ringgit obtained for 1 pound
  • USD per MYR = dollars obtained for 1 ringgit

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the triangular arbitrage calculator on the Module 12 page. It is useful for checking both directions of the currency loop.
Show detailed solution
  1. Go one leg at a time. First convert dollars into pounds: $1,500 / 1.50 = £1,000.
  2. Now convert pounds into ringgit using the cross rate: £1,000 × 6.1 = MYR 6,100.
  3. Now convert ringgit back into dollars: MYR 6,100 × 0.25 = $1,525.
  4. Compare the ending dollars with the starting dollars: 1,525 − 1,500 = 25.
  5. Because the loop ends with more money than it started, this direction is profitable.
Answer: Yes, triangular arbitrage exists. Profit = $25. On an exam, say clearly which direction works.

Problem 12 — Module 13: FX option payoff and profit

Separate payoff from profit.

Long put payoff = max(X − ST, 0)     Long put profit = max(X − ST, 0) − premium
A speculator buys a put option on Swiss francs with strike $0.60 and premium $0.05. At expiration, spot is $0.55. Find payoff and profit per unit.

What the equation means

  • X = strike price
  • ST = spot price at expiration
  • Payoff = value from exercise only, before premium
  • Profit = payoff minus the premium paid

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the FX options payoff game or the Module 13 page to visualize call and put payoff curves. Remember: PUT = DOWN.
Show detailed solution
  1. Because this is a put, the holder benefits when the foreign currency price goes down.
  2. Compare strike and final spot: X − ST = 0.60 − 0.55 = 0.05.
  3. Use the max rule: max(0.05, 0) = 0.05. So the payoff is $0.05 per unit.
  4. Now subtract the premium paid: profit = 0.05 − 0.05 = 0.00.
Answer: Payoff = $0.05 per unit; Profit = $0.00 per unit. This is a good reminder that payoff and profit are not the same.

Problem 13 — Module 14: Importer hedge comparison

Compare forward, money market, and call hedge for a payable.

Forward cost = FC × F
Money market hedge (payable): Deposit today = FC / (1 + if)T; USD today = Deposit today × S; USD cost at T = USD today × (1 + iUS)T
Call hedge: if ST > K, cost = FC × (K + p); if ST ≤ K, cost = FC × ST + FC × p
A U.S. importer must pay R$10,000 in 30 days. Spot is 0.200 USD/BRL, forward is 0.205 USD/BRL, Brazilian 30-day rate is 1%, U.S. 30-day rate is 0.5%, call strike is 0.204, call premium is 0.004, and the assumed future spot is 0.210. Which hedge gives the lowest cost in this scenario?

What the equation means

  • FC = foreign-currency payable
  • F = forward rate
  • S = spot rate today
  • i_f = foreign interest rate for the same horizon
  • i_US = U.S. interest rate for the same horizon
  • K = call strike
  • p = call premium per unit
  • ST = future spot used in the option scenario

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the hedge calculators on the Module 14 page. That page compares Forward • Money Market • Options for importers and exporters.
Show detailed solution
  1. Start with the forward because it is the easiest: forward cost = 10,000 × 0.205 = $2,050.
  2. Now do the money market hedge. Discount the foreign payable back to today: 10,000 / 1.01 = 9,900.99 BRL.
  3. Buy that amount of BRL today at the spot rate: 9,900.99 × 0.200 = $1,980.20 today.
  4. Grow that dollar amount forward for 30 days at the U.S. rate: 1,980.20 × 1.005 ≈ $1,990.10.
  5. Now test the call hedge. Because the future spot 0.210 is above the strike 0.204, exercise the call.
  6. Call hedge cost = 10,000 × (0.204 + 0.004) = 10,000 × 0.208 = $2,080.
  7. Compare the three dollar costs: forward = 2,050; money market ≈ 1,990.10; call = 2,080.
Scenario comparison: Forward = $2,050, Money market ≈ $1,990.10, Call = $2,080. Best in this scenario: money market hedge.

Problem 14 — Module 14: Exporter hedge comparison

Compare forward, money market, and put hedge for a receivable.

Forward revenue = FC × F
Money market hedge (receivable): Borrow FC today = FC / (1 + if)T; convert now at spot; invest dollars until T
Put hedge: if ST < K, revenue = FC × (K − p); if ST ≥ K, revenue = FC × ST − FC × p
A U.S. exporter will receive £50,000 in 90 days. Spot is 1.30 USD/£, forward is 1.29 USD/£, U.K. 90-day rate is 1%, U.S. 90-day rate is 0.5%, put strike is 1.28, premium is 0.02, and the expected future spot is 1.24. Which hedge gives the highest dollar revenue in this scenario?

What the equation means

  • FC = foreign-currency receivable
  • F = forward rate
  • S = spot rate today
  • i_f = foreign interest rate
  • K = put strike
  • p = put premium per unit
  • ST = future spot in the scenario

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance tool: Use the exporter section of the Module 14 hedge calculators for forward, money market, and put comparisons.
Show detailed solution
  1. Start with the forward: 50,000 × 1.29 = $64,500.
  2. Now do the money market hedge. Borrow the present value of the pound receivable today: 50,000 / 1.01 = 49,504.95 pounds.
  3. Convert that amount into dollars now: 49,504.95 × 1.30 = $64,356.44.
  4. Invest those dollars for 90 days at the U.S. rate: 64,356.44 × 1.005 ≈ $64,678.22.
  5. Now test the put. Because the future spot 1.24 is below the strike 1.28, exercise the put.
  6. Put hedge revenue = 50,000 × (1.28 − 0.02) = 50,000 × 1.26 = $63,000.
  7. Compare the three revenues: forward = 64,500; money market ≈ 64,678.22; put = 63,000.
Scenario comparison: Forward = $64,500, Money market ≈ $64,678.22, Put = $63,000. Best in this scenario: money market hedge.

Problem 15 — Module 15: Plain vanilla swap effective cost

Net the original borrowing and swap cash flows carefully.

Effective cost = Original borrowing cost + What the firm pays in the swap − What the firm receives in the swap
Company A wants floating-rate debt. It can borrow directly at LIBOR + 0.30%, or it can borrow fixed at 10.0%. In the swap, A pays LIBOR + 0.55% and receives fixed 10.5%. Find A’s effective borrowing cost after the swap and the savings versus direct floating borrowing.

What the equation means

  • Original borrowing cost = rate the firm pays on the debt it actually issues first
  • Swap paid = cash-flow leg the firm sends to the counterparty
  • Swap received = cash-flow leg the firm receives from the counterparty
  • Effective cost = net rate after combining the borrowing and the swap

Before you calculate

  • Say what the quote means in words.
  • Decide which country is on the quoted-currency side and which is on the base-currency side.
  • Then plug the numbers into the equation in the same order.
JUFinance note: Module 15 is your swaps page. Use the Module 15 page if it is live on your site. If not, this worked example is the clearest exam-style template: borrow first, then add swap paid, then subtract swap received.
Show detailed solution
  1. Start with the borrowing A actually chooses before the swap: fixed at 10.0%.
  2. Now add what A pays in the swap: LIBOR + 0.55%.
  3. Then subtract what A receives in the swap: 10.5%.
  4. Write the full net expression: effective cost = 10.0% + (LIBOR + 0.55%) − 10.5%.
  5. Combine the fixed parts: 10.0% − 10.5% + 0.55% = 0.05%.
  6. So the effective cost becomes LIBOR + 0.05%.
  7. Compare with direct floating borrowing at LIBOR + 0.30%.
  8. Savings = 0.30% − 0.05% = 0.25%.
Answer: Effective borrowing cost = LIBOR + 0.05%. Company A saves 0.25% versus borrowing floating directly.

Fast formula list for the final

FX / parity / arbitrage

PPP: E[S1] = S0 × (1 + π_home)/(1 + π_foreign) IFE: E[S1] = S0 × (1 + i_home)/(1 + i_foreign) IRP: F = S × (1 + i_q × T)/(1 + i_b × T) Locational arbitrage: buy at lower ask, sell at higher bid Triangular arbitrage: test the full loop one leg at a time

Derivatives / hedging

Long call payoff = max(ST − X, 0) Long put payoff = max(X − ST, 0) Profit = payoff − premium (for buyer) Forward hedge = amount × forward rate Swap effective cost = original borrowing + swap paid − swap received
Last reminder: in almost every calculation problem, the math itself is not the hardest part. The hardest part is choosing the correct equation and using the quote direction correctly.