Math Problem Statement

A bank is quoting the following exchange rates against the dollar for the Swiss franc and the Australian dollar:

SFr/$ = 1.5960 − 70

A$/$ = 1.7225 − 35

An Australian firm asks the bank for an A$/SFr quote. What cross-rate would the bank quote?

Solution

To calculate the cross-rate between Australian dollars (A$) and Swiss francs (SFr), we will use the given exchange rates for Swiss francs and Australian dollars against the US dollar (USD). The general formula for cross-rates is:

Cross rate(A$/SFr)=A$/USDSFr/USD\text{Cross rate} \, (A\$/SFr) = \frac{\text{A\$/USD}}{\text{SFr/USD}}

We are given the following exchange rates:

  • Swiss francs against USD (SFr/USD) = 1.5960 − 1.5970
  • Australian dollars against USD (A$/USD) = 1.7225 − 1.7260

Now, let's compute the A$/SFr cross-rates for both the bid and ask prices:

1. Bid Price for A$/SFr:

  • Bid price for A$/SFr = (Bid price of A$/USD) ÷ (Ask price of SFr/USD)
  • Bid = 1.72251.5970\frac{1.7225}{1.5970}

2. Ask Price for A$/SFr:

  • Ask price for A$/SFr = (Ask price of A$/USD) ÷ (Bid price of SFr/USD)
  • Ask = 1.72601.5960\frac{1.7260}{1.5960}

Let me calculate these values for you.The cross-rate the bank would quote for A$/SFr is:

  • Bid price: 1.0786 A$/SFr
  • Ask price: 1.0815 A$/SFr

Would you like more details or have any further questions?

Here are 5 related questions you might find helpful:

  1. How do cross-rates affect international trade?
  2. What is the significance of the bid-ask spread in currency exchange?
  3. How do exchange rates influence a company’s foreign earnings?
  4. What factors determine the fluctuations in cross-currency rates?
  5. How are exchange rates set by banks in different countries?

Tip: Understanding how bid and ask prices work in exchange rates is crucial for getting the best deal in currency conversion. Always aim to understand the spread!

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Math Problem Analysis

Mathematical Concepts

Cross-rates
Bid-Ask Spread
Currency Exchange

Formulas

Cross rate (A$/SFr) = A$/USD ÷ SFr/USD
Bid Price for A$/SFr = (Bid price of A$/USD) ÷ (Ask price of SFr/USD)
Ask Price for A$/SFr = (Ask price of A$/USD) ÷ (Bid price of SFr/USD)

Theorems

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Suitable Grade Level

Grades 11-12 (Advanced Finance/Math)