🌐 Economics

Exchange Rate Calculations — Forward Rates & Interest Rate Parity

Exchange rate formulas: spot rates, forward rates, cross rates, and covered interest rate parity. How to calculate forward exchange rates with examples.

Key Concepts

Exchange Rate Quotation

Direct: domestic per foreign (e.g., 1.25 USD/EUR). Indirect: foreign per domestic. Price/Base convention: P/B.

Bid-Ask Spread

Dealer buys at bid, sells at ask. Spread = ask - bid. Always buy high (ask) and sell low (bid) from YOUR perspective.

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Formulas

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Cross Rate

A/C = (A/B) × (B/C)

Where: Multiply rates to find the cross rate

Forward Rate (CIP)

F/S = (1 + rprice) / (1 + rbase)

Where: F = forward, S = spot, r = interest rate for the period

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Master Formula Sheet -- Economics

GDP (Expenditure)

GDP = C + I + G + (X - M)

Consumption + Investment + Government + Net Exports

Fiscal Multiplier

Multiplier = 1 / (1 - MPC)

MPC = marginal propensity to consume

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Decision Frameworks

How to determine if arbitrage exists?

Use when:

  • Compare calculated cross rate to market cross rate
  • If different, buy low and sell high through the triangle
  • Forward rate vs spot × interest rate differential for covered interest arbitrage

Avoid when:

  • Ignoring transaction costs which may eliminate the arbitrage profit

Test Your Understanding

If the USD/EUR spot rate is 1.10 and the 1-year US interest rate exceeds the EUR rate, the forward USD/EUR rate will be:

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