High School Maths · Year 2 · Unit 14 · Lesson 4 of 5

Hire Purchase and Loans: The Real Cost of Paying Later

About 15 minutes · cash price, deposit and instalments · total hire purchase (HP) price · extra cost and percentage extra · finding an instalment or a deposit · loan repayments with simple interest · comparing ways to pay · no calculator · exit quiz

Hook

A sofa costs $900 cash. Or you can pay $90 now, and then $40 a month for 24 months.

Which way costs less, and by how much?

Paying cash, by $150. On the monthly plan you pay 90 + 24 × 40 = 90 + 960 = $1,050. That is $150 more than the cash price. This way of paying is called hire purchase (HP): you pay extra for the chance to pay later.

Learn

Master the essentials

Cash price

The price if you pay all of it at once.

Cash price: $800

Deposit

The amount paid at the start. It is often a percentage of the cash price.

15% of $800 = $120

Instalments

Equal payments, usually made every month.

12 × $65 = $780

Total HP price

Total paid = deposit + all the instalments.

$120 + $780 = $900

Extra cost

Extra cost = total HP price − cash price.

$900 − $800 = $100

Percentage extra

Extra cost ÷ CASH price × 100.

100 ÷ 800 × 100 = 12.5%

Finding an instalment

Amount still to pay ÷ number of instalments.

$1,440 over 24 months: $60 a month

Loan repayments

Total to repay = loan + interest. Each repayment = total ÷ number of repayments.

$3,000 at 8% simple interest for 2 years, paid monthly: (3,000 + 480) ÷ 24 = $145

Worked examples

See it done

1. A fridge has a cash price of $1,200. On HP you pay a 25% deposit and 18 monthly payments of $56. Find the extra cost of HP and the percentage extra.

  1. Deposit: 25% of 1,200 = $300.
  2. Instalments: 18 × 56 = $1,008.
  3. Total HP price: 300 + 1,008 = $1,308.
  4. Extra cost: 1,308 − 1,200 = $108. Percentage extra: 108 ÷ 1,200 × 100 = 9%.

$108 extra, which is 9%

2. A cooker has a cash price of $640. On HP you pay a $100 deposit. The rest, plus 15% interest on it, is paid in 12 equal monthly instalments. Find each instalment.

  1. Still to pay: 640 − 100 = $540.
  2. Add 15% interest: 10% = 54 and 5% = 27, so 540 + 81 = $621.
  3. Each instalment: 621 ÷ 12 = $51.75.

$51.75

3. Tom borrows $5,400 at 6% simple interest per year for 3 years. He repays it in equal monthly amounts. Find each monthly repayment.

  1. Interest: 5,400 × 6 × 3 ÷ 100 = $972.
  2. Total to repay: 5,400 + 972 = $6,372.
  3. 3 years = 36 months.
  4. Each repayment: 6,372 ÷ 36 = $177.

$177

Common mistake: Forgetting the deposit when finding the total HP price, and working out the percentage extra out of the HP price. The percentage extra is always out of the CASH price.

PractiseNo calculator

10 questions with instant feedback

Choose the correct answer. No calculator. Write down the deposit, the instalments and the total before you compare. Questions 1–3 are warm-ups, 4–7 are at exam standard and 8–10 are challenge questions. After you answer, the feedback shows the full solution.

Score: 0 / 10Answered: 0 / 10

Warm-up (The basic skill: one or two steps.)

1.On HP, a TV costs a $135 deposit and 10 monthly payments of $45. What is the total HP price?

Not quite. This forgets the deposit.

Solution

  1. Payments: 10 × 45 = $450.
  2. Total: 135 + 450 = $585.

Answer: C. $585.

Not quite. This adds only one monthly payment. There are 10.

Solution

  1. Payments: 10 × 45 = $450.
  2. Total: 135 + 450 = $585.

Answer: C. $585.

Correct.

Solution

  1. Payments: 10 × 45 = $450.
  2. Total: 135 + 450 = $585.

Not quite. This pays the deposit 10 times as well. The deposit is paid once.

Solution

  1. Payments: 10 × 45 = $450.
  2. Total: 135 + 450 = $585.

Answer: C. $585.

2.A guitar has a cash price of $460. On HP a 15% deposit is needed. How much is the deposit, and how much is left to pay?

Not quite. This adds the deposit. The deposit comes off what is left to pay.

Solution

  1. 10% of 460 = 46 and 5% = 23, so 15% = $69.
  2. Left to pay: 460 − 69 = $391.

Answer: C. Deposit $69; $391 left to pay.

Not quite. This takes $15, not 15%.

Solution

  1. 10% of 460 = 46 and 5% = 23, so 15% = $69.
  2. Left to pay: 460 − 69 = $391.

Answer: C. Deposit $69; $391 left to pay.

Correct.

Solution

  1. 10% of 460 = 46 and 5% = 23, so 15% = $69.
  2. Left to pay: 460 − 69 = $391.

Not quite. This swaps them round: $391 is 85% of the price.

Solution

  1. 10% of 460 = 46 and 5% = 23, so 15% = $69.
  2. Left to pay: 460 − 69 = $391.

Answer: C. Deposit $69; $391 left to pay.

3.A loan of $2,400 at 5% simple interest per year for 2 years is repaid in 24 equal monthly payments. Find each payment.

Not quite. This forgets the interest.

Solution

  1. Interest: 2,400 × 5 × 2 ÷ 100 = $240.
  2. Total: 2,400 + 240 = $2,640.
  3. Each payment: 2,640 ÷ 24 = $110.

Answer: D. $110.

Not quite. This adds only one year of interest. The loan is for 2 years.

Solution

  1. Interest: 2,400 × 5 × 2 ÷ 100 = $240.
  2. Total: 2,400 + 240 = $2,640.
  3. Each payment: 2,640 ÷ 24 = $110.

Answer: D. $110.

Not quite. This is the total to repay. Divide it by 24.

Solution

  1. Interest: 2,400 × 5 × 2 ÷ 100 = $240.
  2. Total: 2,400 + 240 = $2,640.
  3. Each payment: 2,640 ÷ 24 = $110.

Answer: D. $110.

Correct.

Solution

  1. Interest: 2,400 × 5 × 2 ÷ 100 = $240.
  2. Total: 2,400 + 240 = $2,640.
  3. Each payment: 2,640 ÷ 24 = $110.

Exam standard (Several steps, like real exam questions.)

4.The table shows two plans for buying a laptop with a cash price of $1,500. Which plan costs less in total, and by how much?

PlanDepositMonthly payments
X$30012 payments of $110
Y10% of the cash price24 payments of $62

Two ways to pay for a laptop with a cash price of $1,500.

Correct.

Solution

  1. Plan X: 300 + 12 × 110 = 300 + 1,320 = $1,620.
  2. Plan Y: 150 + 24 × 62 = 150 + 1,488 = $1,638.
  3. Plan X costs $18 less.

Not quite. This uses a deposit of $10. The deposit is 10% of $1,500 = $150.

Solution

  1. Plan X: 300 + 12 × 110 = 300 + 1,320 = $1,620.
  2. Plan Y: 150 + 24 × 62 = 150 + 1,488 = $1,638.
  3. Plan X costs $18 less.

Answer: A. Plan X, by $18.

Not quite. This forgets the deposit in plan Y.

Solution

  1. Plan X: 300 + 12 × 110 = 300 + 1,320 = $1,620.
  2. Plan Y: 150 + 24 × 62 = 150 + 1,488 = $1,638.
  3. Plan X costs $18 less.

Answer: A. Plan X, by $18.

Not quite. This forgets both deposits.

Solution

  1. Plan X: 300 + 12 × 110 = 300 + 1,320 = $1,620.
  2. Plan Y: 150 + 24 × 62 = 150 + 1,488 = $1,638.
  3. Plan X costs $18 less.

Answer: A. Plan X, by $18.

5.A washing machine has a cash price of $560. On HP it costs a $112 deposit and 12 monthly payments of $42. Find the percentage extra paid on HP.

Not quite. This divides by the HP price. The percentage extra is out of the cash price.

Solution

  1. Payments: 12 × 42 = $504. Total: 112 + 504 = $616.
  2. Extra cost: 616 − 560 = $56.
  3. 56 ÷ 560 × 100 = 10%.

Answer: B. 10%.

Correct.

Solution

  1. Payments: 12 × 42 = $504. Total: 112 + 504 = $616.
  2. Extra cost: 616 − 560 = $56.
  3. 56 ÷ 560 × 100 = 10%.

Not quite. $56 is the extra cost in dollars, not the percentage.

Solution

  1. Payments: 12 × 42 = $504. Total: 112 + 504 = $616.
  2. Extra cost: 616 − 560 = $56.
  3. 56 ÷ 560 × 100 = 10%.

Answer: B. 10%.

Not quite. 616 ÷ 560 = 1.1 means the HP price is 110% of the cash price: 10% extra.

Solution

  1. Payments: 12 × 42 = $504. Total: 112 + 504 = $616.
  2. Extra cost: 616 − 560 = $56.
  3. 56 ÷ 560 × 100 = 10%.

Answer: B. 10%.

6.An HP agreement has a $250 deposit and 15 equal monthly payments. The total HP price is $1,600. How much is each monthly payment?

Correct.

Solution

  1. Paid by instalments: 1,600 − 250 = $1,350.
  2. Each payment: 1,350 ÷ 15 = $90.

Not quite. This forgets to take off the deposit first.

Solution

  1. Paid by instalments: 1,600 − 250 = $1,350.
  2. Each payment: 1,350 ÷ 15 = $90.

Answer: A. $90.

Not quite. This adds the deposit. It should be taken off.

Solution

  1. Paid by instalments: 1,600 − 250 = $1,350.
  2. Each payment: 1,350 ÷ 15 = $90.

Answer: A. $90.

Not quite. This is the total of the monthly payments. Divide it by 15.

Solution

  1. Paid by instalments: 1,600 − 250 = $1,350.
  2. Each payment: 1,350 ÷ 15 = $90.

Answer: A. $90.

7.A phone has a cash price of $720. On HP there is a 20% deposit and 12 monthly payments of $52. Which working shows that HP costs $48 more than cash?

Not quite. The deposit is 20% of $720 = $144, not $20.

Solution

  1. Deposit: 20% of 720 = $144.
  2. Total HP price: 144 + 12 × 52 = 144 + 624 = $768.
  3. Extra: 768 − 720 = $48 ✓.

Answer: D. 144 + 12 × 52 − 720 = 48.

Not quite. This leaves out the deposit.

Solution

  1. Deposit: 20% of 720 = $144.
  2. Total HP price: 144 + 12 × 52 = 144 + 624 = $768.
  3. Extra: 768 − 720 = $48 ✓.

Answer: D. 144 + 12 × 52 − 720 = 48.

Not quite. This is the total HP price. It does not take away the cash price to show the extra.

Solution

  1. Deposit: 20% of 720 = $144.
  2. Total HP price: 144 + 12 × 52 = 144 + 624 = $768.
  3. Extra: 768 − 720 = $48 ✓.

Answer: D. 144 + 12 × 52 − 720 = 48.

Correct.

Solution

  1. Deposit: 20% of 720 = $144.
  2. Total HP price: 144 + 12 × 52 = 144 + 624 = $768.
  3. Extra: 768 − 720 = $48 ✓.

Challenge (Harder problems that mix ideas or need reasoning.)

8.Kai borrows $6,000. He repays $280 a month for 2 years. What rate of simple interest per year is he charged?

Not quite. This is the interest for both years. Divide by 2 for the rate per year.

Solution

  1. Total repaid: 280 × 24 = $6,720.
  2. Interest: 6,720 − 6,000 = $720, so $360 a year.
  3. Rate: 360 ÷ 6,000 × 100 = 6% per year.

Answer: B. 6%.

Correct.

Solution

  1. Total repaid: 280 × 24 = $6,720.
  2. Interest: 6,720 − 6,000 = $720, so $360 a year.
  3. Rate: 360 ÷ 6,000 × 100 = 6% per year.

Not quite. This divides by the total repaid, $6,720. The rate is worked out on the $6,000 borrowed.

Solution

  1. Total repaid: 280 × 24 = $6,720.
  2. Interest: 6,720 − 6,000 = $720, so $360 a year.
  3. Rate: 360 ÷ 6,000 × 100 = 6% per year.

Answer: B. 6%.

Not quite. This is the rate per month. The question asks for the rate per year.

Solution

  1. Total repaid: 280 × 24 = $6,720.
  2. Interest: 6,720 − 6,000 = $720, so $360 a year.
  3. Rate: 360 ÷ 6,000 × 100 = 6% per year.

Answer: B. 6%.

9.A bike has a cash price of $2,600. Plan 1: HP with a 10% deposit and 24 payments of $115. Plan 2: a loan of $2,600 at 7% simple interest per year for 2 years. Which plan costs less, and by how much?

Not quite. This adds only one year of interest to the loan. The loan is for 2 years.

Solution

  1. Plan 1: 260 + 24 × 115 = 260 + 2,760 = $3,020.
  2. Plan 2: interest = 2,600 × 7 × 2 ÷ 100 = $364, so $2,964.
  3. Plan 2 costs 3,020 − 2,964 = $56 less.

Answer: C. Plan 2, by $56.

Not quite. This forgets the HP deposit of $260.

Solution

  1. Plan 1: 260 + 24 × 115 = 260 + 2,760 = $3,020.
  2. Plan 2: interest = 2,600 × 7 × 2 ÷ 100 = $364, so $2,964.
  3. Plan 2 costs 3,020 − 2,964 = $56 less.

Answer: C. Plan 2, by $56.

Correct.

Solution

  1. Plan 1: 260 + 24 × 115 = 260 + 2,760 = $3,020.
  2. Plan 2: interest = 2,600 × 7 × 2 ÷ 100 = $364, so $2,964.
  3. Plan 2 costs 3,020 − 2,964 = $56 less.

Not quite. This uses compound interest. The loan has simple interest.

Solution

  1. Plan 1: 260 + 24 × 115 = 260 + 2,760 = $3,020.
  2. Plan 2: interest = 2,600 × 7 × 2 ÷ 100 = $364, so $2,964.
  3. Plan 2 costs 3,020 − 2,964 = $56 less.

Answer: C. Plan 2, by $56.

10.A drum kit has a cash price of $1,000. On HP it costs $1,180: a deposit and then 20 monthly payments of $47. What is the deposit as a percentage of the cash price?

Not quite. This is the percentage extra for HP, not the deposit.

Solution

  1. Payments: 20 × 47 = $940.
  2. Deposit: 1,180 − 940 = $240.
  3. 240 ÷ 1,000 × 100 = 24%.

Answer: B. 24%.

Correct.

Solution

  1. Payments: 20 × 47 = $940.
  2. Deposit: 1,180 − 940 = $240.
  3. 240 ÷ 1,000 × 100 = 24%.

Not quite. This divides the deposit by the HP price. The question asks for a percentage of the cash price.

Solution

  1. Payments: 20 × 47 = $940.
  2. Deposit: 1,180 − 940 = $240.
  3. 240 ÷ 1,000 × 100 = 24%.

Answer: B. 24%.

Not quite. This takes the payments away from the cash price. Take them away from the HP price, $1,180.

Solution

  1. Payments: 20 × 47 = $940.
  2. Deposit: 1,180 − 940 = $240.
  3. 240 ÷ 1,000 × 100 = 24%.

Answer: B. 24%.

Apply

Choosing how to pay

A scooter has a cash price of $1,800. Option 1 is HP: a $360 deposit and 18 monthly payments of $92. Option 2 is a loan of $1,800 at 7% simple interest per year, repaid in 18 equal monthly payments.

1. Find the total HP price, the extra cost and the percentage extra for option 1.

2. Find the monthly repayment for option 2.

3. Which option costs less in total, and by how much?

  1. Payments: 18 × 92 = $1,656. Total: 360 + 1,656 = $2,016. Extra: 2,016 − 1,800 = $216, which is 216 ÷ 1,800 × 100 = 12%.
  2. 18 months = 1.5 years. Interest: 1,800 × 7 × 1.5 ÷ 100 = $189. Total: $1,989. Each repayment: 1,989 ÷ 18 = $110.50.
  3. Option 2 costs $1,989 and option 1 costs $2,016, so the loan is cheaper by $27.

Next: the Lesson 4 exit quiz. Five questions, recorded on your dashboard. Aim for 4 out of 5.

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