Commercial arithmetic: hire purchase — KCSE Mathematics

KCSE Mathematics · 115 practice questions · 3 syllabus objectives · 3 revision lessons

39 easy39 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.

Define hire purchase; calculate the hire purchase price, deposit, monthly instalment and total interest paid

Compare the hire purchase price with the cash price to determine the extra cost of buying on hire purchase

Commercial arithmetic: hire purchase

Revision Notes

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

Understanding Hire Purchase in Mathematics

Hire purchase is a method of buying goods through an initial deposit followed by regular monthly payments. The total cost of the item is paid over time, which includes interest. To calculate the hire purchase price, follow these steps:

  1. Deposit: This is the initial amount paid upfront, usually a percentage of the total price.
  2. Hire Purchase Price: This is the total amount payable, including the cost of the item plus interest.
  3. Monthly Instalment: This is the amount paid each month, calculated by dividing the total amount payable minus the deposit by the number of months.
  4. Total Interest Paid: This is the difference between the hire purchase price and the cash price of the item.

For example, if a television costs Ksh 50,000, and a 20% deposit is paid:

  • Deposit = 20% of 50,000 = Ksh 10,000
  • Remaining amount = 50,000 - 10,000 = Ksh 40,000
  • If the total hire purchase price is Ksh 60,000, then Total Interest Paid = 60,000 - 50,000 = Ksh 10,000
  • Monthly Instalment = (60,000 - 10,000) / 24 months = Ksh 2,083.33.

Key points to remember

  • Hire purchase involves deposit and monthly payments.
  • Total hire purchase price includes interest.
  • Monthly instalment is calculated over the payment period.
  • Total interest paid is the difference from cash price.

Worked example

A fridge costs Ksh 80,000 with a 15% deposit. Calculate the deposit, hire purchase price, and monthly instalment for 24 months.

  • Deposit = 15% of 80,000 = Ksh 12,000.
  • Hire Purchase Price = 80,000 + Interest = Ksh 100,000.
  • Monthly Instalment = (100,000 - 12,000) / 24 = Ksh 3,666.67.

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More lessons in this topic

Lesson 2: Understanding Hire Purchase Costs

Objective: Compare the hire purchase price with the cash price to determine the extra cost of buying on hire purchase

In hire purchase agreements, consumers can acquire goods by paying an initial deposit followed by regular installments. To evaluate the financial impact, it is crucial to compare the hire purchase price with the cash price.

Steps to Determine Extra Cost:

  1. Identify Cash Price: This is the total amount payable if the item is bought outright.
  2. Identify Hire Purchase Price: This is the total cost when purchasing through hire purchase, including interest and fees.
  3. Calculate Extra Cost: Subtract the cash price from the hire purchase price.

Formula:
Extra Cost = Hire Purchase Price - Cash Price

For example, if a television has a cash price of KSh 30,000 and a hire purchase price of KSh 36,000:

  • Extra Cost = KSh 36,000 - KSh 30,000
  • Extra Cost = KSh 6,000

This means the consumer pays an additional KSh 6,000 for buying on hire purchase. Understanding these costs helps consumers make informed financial decisions.

  • Hire purchase allows payment in installments.
  • Cash price is the total upfront cost.
  • Hire purchase price includes interest and fees.
  • Extra cost is the difference between hire purchase and cash prices.
  • Informed decisions require comparing total costs.

A fridge costs KSh 25,000 cash. The hire purchase price is KSh 30,000. Calculate the extra cost.

  • Extra Cost = KSh 30,000 - KSh 25,000
  • Extra Cost = KSh 5,000.
Lesson 3: Understanding Hire Purchase in Commercial Arithmetic

Objective: Commercial arithmetic: hire purchase

Hire purchase is a method of buying goods through installment payments. In this arrangement, the buyer pays a deposit and then pays the remaining balance in installments over time. The total cost often includes interest, which is an additional charge for the convenience of paying in installments.

Key components of hire purchase:

  • Deposit: Initial payment made at the time of purchase.
  • Installments: Regular payments made after the deposit.
  • Total cost: The sum of the deposit, installments, and any interest charged.

To calculate the total cost of a hire purchase agreement, use the formula:

Total Cost = Deposit + (Number of Installments × Installment Amount) + Interest

For example, if you buy a television for Ksh 30,000 with a deposit of Ksh 10,000, and you agree to pay Ksh 5,000 per month for 5 months, plus Ksh 2,500 interest, the total cost would be:

Total Cost = 10,000 + (5 × 5,000) + 2,500 = 10,000 + 25,000 + 2,500 = Ksh 37,500.

  • Hire purchase allows payment in installments over time.
  • Total cost includes deposit, installments, and interest.
  • Calculate total cost using the provided formula.

A laptop costs Ksh 60,000, with a deposit of Ksh 20,000 and monthly installments of Ksh 8,000 for 5 months. Calculate the total cost.

Total Cost = 20,000 + (5 × 8,000) = 20,000 + 40,000 = Ksh 60,000.

Sample Questions

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1
easySHORT ANSWER4 marks

A motorbike has a cash price of Ksh 80,000. If bought on hire purchase, there is a deposit of Ksh 16,000 followed by 18 monthly instalments of Ksh 5,000. (a) Calculate the total hire purchase price. (2 marks) (b) Find the extra amount paid compared to the cash price. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
Total HP = 16000 + (18 × 5000) (1 mk)
Correct total HP = Ksh 106,000 (1 mk)
Part (b) — 2 marks
Extra amount = 106000 - 80000 (1 mk)
Correct extra amount = Ksh 26,000 (1 mk)
2
easySHORT ANSWER4 marks

A laptop is available for Ksh 60,000 cash. If bought on hire purchase, a deposit of Ksh 12,000 is paid followed by 15 monthly instalments of Ksh 4,000. (a) Find the hire purchase price. (2 marks) (b) What is the total extra cost incurred when buying on hire purchase? (2 marks)

Answer & marking scheme

Part (a) — 2 marks
HP = 12000 + (15 × 4000) (1 mk)
Correct HP = Ksh 72,000 (1 mk)
Part (b) — 2 marks
Extra cost = 72000 - 60000 (1 mk)
Correct extra cost = Ksh 12,000 (1 mk)
3
easySHORT ANSWER4 marks

A television set has a cash price of Ksh 40,000. It can be purchased on hire purchase by paying a deposit of Ksh 8,000 followed by 12 monthly instalments of Ksh 3,000 each. (a) Calculate the total hire purchase price. (2 marks) (b) Determine the extra amount paid compared to the cash price. (2 marks)

Answer & marking scheme

Part (a) — 2 marks
Total HP = 8000 + (12 × 3000) (1 mk)
Correct total HP = Ksh 44,000 (1 mk)
Part (b) — 2 marks
Extra amount = 44000 - 40000 (1 mk)
Correct extra amount = Ksh 4,000 (1 mk)
4

A television set has a cash price of Ksh 80,000. The buyer pays a deposit of Ksh 20,000 and then pays Ksh 5,000 per month for 12 months. (a) State the total hire purchase price. (2 marks) (b) Calculate the total interest paid on the hire purchase. (2 marks)

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Frequently asked questions

What does the KCSE Mathematics topic "Commercial arithmetic: hire purchase" cover?

Commercial arithmetic: hire purchase covers Define hire purchase; calculate the hire purchase price, deposit, monthly instalment and total interest paid; Compare the hire purchase price with the cash price to determine the extra cost of buying on hire purchase; Commercial arithmetic: hire purchase, all aligned to the official KNEC KCSE Mathematics syllabus.

How many practice questions are available for Commercial arithmetic: hire purchase?

HighMarks has 115 Commercial arithmetic: hire purchase 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: hire purchase for the KCSE exam?

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