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Hire Purchase

Consumer Arithmetic · Interest and Installment Buying

Handro Learning was founded by Randy Sonson in 2014, after years of online tutoring revealed that many students struggle with the same Mathematics topics simply from a lack of exposure and practice. This platform gives students access to clear explanations and practice questions any time they need, to review a topic or test their understanding, not just during a scheduled lesson.

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Hire purchase is a way of buying an item by paying part of the price first, then paying the rest in equal payments over time.

The first payment is called a deposit. The equal payments made after that are called instalments.

Hire purchase usually costs more than paying cash. The extra amount is the money saved if the item is bought for cash instead.

What You Will Learn

  • Understand what hire purchase means
  • Calculate the total hire purchase price
  • Compare the hire purchase price with the cash price
  • Find how much money is saved by paying cash
  • Calculate a deposit given as a percentage of the cash price
  • Work backwards to find an unknown instalment amount

Key Words

  • Cash price: the price paid if the item is bought at once.
  • Deposit: the first payment made before the instalments begin.
  • Instalments: equal payments made over a period of time.
  • Hire purchase price: the total amount paid using hire purchase.

Key Ideas

  • Hire purchase price = deposit + total instalments.
  • Total instalments = number of instalments × amount of each instalment.
  • Amount saved by paying cash = hire purchase price − cash price.
  • A deposit is sometimes given as a percentage of the cash price, and must be converted to a dollar amount first.
  • In most CSEC questions, hire purchase costs more than paying cash.

Main Formulas

Hire purchase price = deposit + (number of instalments × instalment amount)
Amount saved by paying cash = hire purchase price − cash price

TV with Price Tag

Cash $350 A TV can be bought for cash or on hire purchase.
A price tag may show the cash price, while hire purchase uses a deposit and instalments.

Worked Examples

Example 1: The cash price of a television set is $350. On hire purchase, a deposit of $35 is required, followed by 12 monthly payments of $30 each. How much is saved by paying cash?

  1. Deposit = $35
  2. Number of instalments = 12
  3. Each instalment = $30
  4. Total instalments = 12 × 30 = $360
  5. Hire purchase price = 35 + 360 = $395
  6. Cash price = $350
  7. Amount saved by paying cash = 395 − 350 = 45

Answer: $45 saved by paying cash

Example 2: A fridge has a cash price of $2000. On hire purchase, a $400 deposit is paid, followed by 12 monthly payments of $150. Find the hire purchase price and the amount saved by paying cash.

  1. Deposit = $400
  2. Total instalments = 12 × 150 = $1800
  3. Hire purchase price = 400 + 1800 = $2200
  4. Cash price = $2000
  5. Amount saved by paying cash = 2200 − 2000 = $200

Answer: Hire purchase price = $2200; Amount saved = $200

Example 3: A stove is bought with a $300 deposit and 10 payments of $90. Find the hire purchase price.

  1. Deposit = $300
  2. Total instalments = 10 × 90 = $900
  3. Hire purchase price = 300 + 900 = 1200

Answer: $1200

Computer on Hire Purchase

Cash $2500 Paying over time usually makes the total cost higher.
For hire purchase, add the deposit and all instalments to find the total cost.

Example 4: A laptop has a cash price of $2500. On hire purchase, a $500 deposit is paid, followed by 24 payments of $100. How much is saved by paying cash?

  1. Deposit = $500
  2. Total instalments = 24 × 100 = $2400
  3. Hire purchase price = 500 + 2400 = $2900
  4. Cash price = $2500
  5. Amount saved by paying cash = 2900 − 2500 = 400

Answer: $400 saved by paying cash

Example 5: A refrigerator has a cash price of $1600. A deposit of 15% of the cash price is required, followed by 12 monthly instalments of $120 each. Find the hire purchase price and the amount saved by paying cash.

  1. Deposit = 15% of 1600 = 0.15 × 1600 = $240
  2. Total instalments = 12 × 120 = $1440
  3. Hire purchase price = 240 + 1440 = $1680
  4. Cash price = $1600
  5. Amount saved by paying cash = 1680 − 1600 = 80

Answer: Hire purchase price = $1680; Amount saved = $80

When a deposit is given as a percentage, always change it into a dollar amount first, before adding it to the total instalments.

Example 6: A washing machine is bought on hire purchase for a total price of $1750. A deposit of $400 was paid, followed by 18 equal monthly instalments. Find the amount of each instalment.

  1. Hire purchase price = $1750
  2. Deposit = $400
  3. Total instalments = 1750 − 400 = $1350
  4. Number of instalments = 18
  5. Each instalment = 1350 ÷ 18 = 75

Answer: $75 per instalment

To work backwards, first subtract the deposit from the hire purchase price to find the total paid in instalments, then divide by the number of instalments.

Common Mistakes

  • Forgetting to convert a percentage deposit into a dollar amount before adding it to the instalments.
  • Adding the cash price instead of the deposit when finding the hire purchase price.
  • Forgetting to multiply the instalment amount by the number of instalments before adding the deposit.
  • Subtracting in the wrong order when finding the amount saved. It should be hire purchase price − cash price, not the reverse.

Important Reminders

To find the hire purchase price, always add the deposit and all the instalments.
Do not forget to multiply the number of instalments by the amount of each instalment.
The amount saved by paying cash is the difference between the hire purchase price and the cash price.

Practice Questions

  1. 1. A TV is bought on hire purchase with a $250 deposit and 12 monthly payments of $80. Find the total hire purchase price.
  2. 2. The TV in Question 1 has a cash price of $1100. How much is saved by paying cash?
  3. 3. A stove has a cash price of $900. On hire purchase, it needs a $100 deposit and 10 payments of $90. How much is saved by paying cash?
  4. 4. A washing machine has a $400 deposit and 18 payments of $75. Find the hire purchase price.
  5. 5. A computer has a cash price of $3000. On hire purchase, a deposit of $600 is paid, followed by 20 monthly payments of $150. Find the amount saved by paying cash.
  6. 6. A dining set has a cash price of $1200. A deposit of 20% of the cash price is required, followed by 10 monthly instalments of $110. Find the hire purchase price.
  7. 7. A motorbike is bought on hire purchase for a total price of $3200. A deposit of $800 was paid, followed by 16 equal monthly instalments. Find the amount of each instalment.

Answers

  1. $1210
  2. $110
  3. $100
  4. $1750
  5. $600
  6. $1340
  7. $150

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