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Commercial arithmetic: currency exchange — KCSE Mathematics

KCSE Mathematics · 106 practice questions · 3 syllabus objectives · 3 revision lessons

29 easy40 medium37 hard

Last updated · Aligned to the KNEC KCSE syllabus

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Convert between currencies using buying and selling exchange rates from a bank rate table

Calculate the amount received in a foreign currency and the bank charges on currency exchange

Commercial arithmetic: currency exchange

Revision Notes

Concise lesson notes for Commercial arithmetic: currency exchange, written to the KCSE Mathematics marking standard. Read the first lesson free below.

Currency Exchange Conversions

In commercial arithmetic, converting currencies is essential for financial transactions. To convert between currencies, you need to understand buying and selling exchange rates from a bank rate table.

  1. Buying Rate: This is the rate at which the bank buys foreign currency from you.
  2. Selling Rate: This is the rate at which the bank sells foreign currency to you.

To convert from Kenyan Shillings (KES) to a foreign currency, use the selling rate. Conversely, to convert from a foreign currency to KES, use the buying rate.

Example: If the bank's selling rate for USD is 110 KES and the buying rate is 108 KES, to convert 5,500 KES to USD:

  • USD = 5,500 KES ÷ 110 KES/USD = 50 USD.

To convert 50 USD back to KES:

  • KES = 50 USD × 108 KES/USD = 5,400 KES.

Key points to remember

  • Understand buying and selling exchange rates.
  • Use selling rate for KES to foreign currency conversion.
  • Use buying rate for foreign currency to KES conversion.

Worked example

Convert 10,000 KES to EUR if the selling rate is 130 KES/EUR.

  • EUR = 10,000 KES ÷ 130 KES/EUR = 76.92 EUR.

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Lesson 2: Currency Exchange Calculations

Objective: Calculate the amount received in a foreign currency and the bank charges on currency exchange

In commercial arithmetic, currency exchange involves calculating the amount received in a foreign currency after conversion, along with any bank charges. To perform these calculations, follow these steps:

  1. Identify the exchange rate: This is the rate at which your local currency converts to the foreign currency.
  2. Determine the amount to be exchanged: This is the total amount of local currency you want to convert.
  3. Calculate bank charges: Banks may charge a fee for exchanging currency, often as a percentage of the total amount exchanged.
  4. Calculate the final amount in foreign currency: Subtract the bank charges from the total amount exchanged, then apply the exchange rate to find the amount in foreign currency.

Example: If you exchange Ksh 10,000 at an exchange rate of 0.0085 USD/Ksh and the bank charges 2%:

  • Calculate bank charges: 2% of 10,000 = Ksh 200.
  • Amount after charges: 10,000 - 200 = Ksh 9,800.
  • Amount in USD: 9,800 * 0.0085 = USD 83.30.

Thus, you receive USD 83.30 after bank charges.

  • Identify exchange rate and amount to be exchanged.
  • Calculate bank charges as a percentage of the amount.
  • Subtract bank charges from the total amount exchanged.
  • Multiply the net amount by the exchange rate.

If you exchange Ksh 15,000 at 0.009 USD/Ksh with 3% charges, find the amount in USD.

  • Bank charges: 3% of 15,000 = Ksh 450.
  • Net amount: 15,000 - 450 = Ksh 14,550.
  • Amount in USD: 14,550 * 0.009 = USD 130.95.
Lesson 3: Understanding Currency Exchange Rates

Objective: Commercial arithmetic: currency exchange

Currency exchange involves converting one currency into another based on current exchange rates. Key concepts include:

  • Exchange rate: The value of one currency in terms of another.
  • Buying rate: The rate at which a bank buys foreign currency.
  • Selling rate: The rate at which a bank sells foreign currency.

To calculate the amount received when exchanging currency, use the formula:

Amount received = Amount exchanged × Selling rate

For example, if you exchange 100 US dollars to Kenyan shillings at a selling rate of 110 KES/USD, the calculation would be:
Amount received = 100 × 110 = 11,000 KES.

Conversely, to find out how much foreign currency you can get for your local currency, use:
Amount in foreign currency = Amount in local currency ÷ Buying rate.

If you have 10,000 KES and the buying rate is 105 KES/USD, the calculation is:
Amount in foreign currency = 10,000 ÷ 105 ≈ 95.24 USD.

  • Exchange rate determines currency value conversion.
  • Buying and selling rates vary between banks.
  • Use formulas for accurate currency calculations.

If you exchange 200 Euros at a selling rate of 130 KES/EUR, calculate the amount received.
Amount received = 200 × 130 = 26,000 KES.

Sample Questions

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1
easySHORT ANSWER3 marks

A Kenyan student exchanges Ksh 10,000 to obtain Canadian dollars (CAD) at an exchange rate of Ksh 80 per CAD. The bank charges a fee of Ksh 200 for the transaction. Calculate the total amount of Canadian dollars received after deducting the bank charges. (3 marks)

Answer & marking scheme

Part (a) — 1 mark
Available amount = Ksh 10,000 - Ksh 200 (1 mk)
Part (b) — 1 mark
Amount of CAD = Available amount / Ksh 80 (1 mk)
Part (c) — 1 mark
Final amount of CAD = Correct calculation (1 mk)
2
easySHORT ANSWER2 marks

State the amount in Ksh a tourist would get after converting €500 back to Ksh at a selling rate of Ksh 150 per euro. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
Amount in Ksh = €500 × Ksh 150 (1 mk)
Correct value in Ksh (1 mk)
3
easySHORT ANSWER2 marks

State how many euros a Kenyan company would receive after exchanging Ksh 10,000 at a buying rate of Ksh 120 per euro. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
Euros received = Ksh 10,000 / Ksh 120 (1 mk)
Correct value of euros received (1 mk)
4

A tourist converts Ksh 15,000 to US Dollars at an exchange rate of Ksh 130 per Dollar. If the bank charges a fee of Ksh 150, how much US Dollars does the tourist receive? (4 marks)

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Frequently asked questions

What does the KCSE Mathematics topic "Commercial arithmetic: currency exchange" cover?

Commercial arithmetic: currency exchange covers Convert between currencies using buying and selling exchange rates from a bank rate table; Calculate the amount received in a foreign currency and the bank charges on currency exchange; Commercial arithmetic: currency exchange, all aligned to the official KNEC KCSE Mathematics syllabus.

How many practice questions are available for Commercial arithmetic: currency exchange?

HighMarks has 106 Commercial arithmetic: currency exchange practice questions for KCSE Mathematics, each with a full marking scheme. The first 3 are free; sign up to access the rest, plus all KCSE mock exams and past papers.

Are these aligned with the KNEC KCSE syllabus?

Yes. Every objective on this page is taken directly from the official KNEC KCSE Mathematics syllabus. Practice questions match the KCSE exam format and are graded against the standard KNEC marking scheme.

How should I revise Commercial arithmetic: currency exchange for the KCSE exam?

Start with the revision notes on this page to refresh the core concepts, then work through the practice questions in increasing difficulty. Sign up for HighMarks to get a personalised study plan that adapts to the topics you keep getting wrong, plus mock exams, subject-wide practice, and detailed performance tracking. See pricing.

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