Hire Purchase (HP) is a method of buying goods in which the buyer pays an initial deposit (down payment), and then pays the remaining balance through regular instalments over an agreed period.
Under a Hire Purchase agreement, the buyer takes possession of the item immediately after paying the deposit, but legal ownership normally passes to the buyer only after the final instalment has been paid in full.
Hire Purchase is commonly used to purchase expensive items such as motor vehicles, household appliances, furniture, electronics, machinery, and other high-value goods when the buyer is unable or unwilling to pay the full cash price immediately.
The Cash Price (CP) is the full amount of money that must be paid upfront in a single lump sum to buy and own an item immediately.
(i) A refrigerator bought outright for $750 has a cash price of $750.
(ii) A washing machine purchased instantly for $480 has a cash price of $480.
(iii) A delivery van acquired for $18,500 cash has a cash price of $18,500.
The Deposit is the initial down payment made by the buyer to secure the asset and take physical possession of it at the start of a hire purchase contract.
(i) An upfront payment of $150 to secure a smart television has a deposit value of $150.
(ii) A standard commitment fee of 10% paid on a $2,000 item represents a deposit value of $200.
(iii) A mandatory primary down payment of $3,500 on a commercial vehicle has a deposit value of $3,500.
The Hire Purchase Value (HPV), also known as the Hire Purchase Price, is the total amount paid for an item under a hire purchase agreement.
Hire Purchase Value = Deposit + Total Value of Installments
Deposit = $300
Installments = 12 months at $50 per month
Hire Purchase Value = 300 + (12 × 50) = 300 + 600 = $900
The Carrying Charge, commonly referred to as the Hire Purchase Interest or Finance Charge, is the extra amount paid above the Cash Price for purchasing an item on hire purchase.
Interest = Hire Purchase Value − Cash Price
Hire Purchase Value = $1,450
Cash Price = $1,200
Interest = 1,450 − 1,200 = $250
The Monthly Installment is the fixed amount paid at regular intervals (usually every month) after the deposit has been deducted from the Hire Purchase Value.
Monthly Installment = Total Value of installments Number of months
A customer agrees to buy a television on hire purchase. The total value of the installments is $2,160, to be paid over 18 months. Find the monthly installment.
Solution
Total Value of Installments = $2,160
Number of Months = 18
Monthly Installment = 2,160 ÷ 18
Monthly Installment = $120 per month
Hire Purchase Interest Percentage is the percentage of the Cash Price that represents the extra amount paid for buying an item on hire purchase instead of paying the full cash price immediately.
Hire Purchase Interest Percentage = Interest Cash Price × 100%
A motorcycle has a Cash Price of $4,000 and a Hire Purchase Value of $4,600. Find the Hire Purchase Interest Percentage.
Solution
Step 1: Calculate the Hire Purchase Interest.
Hire Purchase Interest = Hire Purchase Value − Cash Price
Hire Purchase Interest = $4,600 − $4,000
Hire Purchase Interest = $600
Since we now have the Hire Purchase Interest, we can use the formula:
Hire Purchase Interest Percentage = Interest Cash Price × 100%
Step 2: Substitute the values into the formula.
Hire Purchase Interest Percentage = $600 $4,000 × 100%
Hire Purchase Interest Percentage = 15%
The cash price of a home theatre system is $1,100. Under hire purchase terms, a customer pays a deposit of $250 followed by 12 monthly installments of $85 each. Find the total hire purchase value and the extra cost incurred over the cash price.
Step 1: Calculate the total value of all monthly installments.
Total Installments = 12 × $85 = $1,020
Step 2: Combine the deposit and installments to find the Hire Purchase Value.
HPV = Deposit + Total Installments
= 250 + 1,020
= 1,270
Step 3: Subtract the Cash Price from the Hire Purchase Value to find the extra cost (interest).
Extra Cost = HPV − Cash Price
= 1,270 − 1,100
= 170
Final Answer: Hire Purchase Value = $1,270, Extra Cost = $170
A designer sofa set has a cash price of $2,400. It can also be purchased on credit terms by paying an initial deposit of 20% of the cash price, plus 18 equal monthly installments. If the total hire purchase value is $2,920, calculate the value of each monthly installment.
Step 1: Calculate the dollar value of the initial 20% deposit based on the cash price.
Deposit = 20% of $2,400
Deposit = 20 100 × 2,400
= 480
Step 2: Isolate the remaining balance assigned to the installments side.
Total Installments = Hire Purchase Value − Deposit
= 2,920 − 480
= 2,440
Step 3: Divide the total installment balance by the number of repayment months.
Monthly Installment = 2,440 ÷ 18
= 135.555...
Final Answer: Monthly Installment = $135.56
A sound editing laptop is offered on hire purchase with a down payment deposit of $400 and 10 consecutive monthly installments of $145 each. If the interest added under this agreement is exactly 16% of the original cash price, calculate the outright cash price of the laptop.
Step 1: Determine the overall hire purchase value.
Total Installments = 10 × 145 = 1,450
HPV = Deposit + Total Installments = 400 + 1,450 = 1,850
Step 2: Set up an algebraic equation relating Cash Price (CP) and Interest.
We know: HPV = CP + Interest
Since Interest = 16% of CP = 0.16 × CP:
1,850 = CP + 0.16CP
1,850 = 1.16CP
Step 3: Solve for the Cash Price .
CP = 1,850 ÷ 1.16
= 1,594.827...
Final Answer: Cash Price = $1,594.83
A print shop plans to buy a high-speed printing machine on hire purchase terms. The cash price is $8,000. The dealer charges a 15% premium interest on the cash price for funding. If the shop pays a deposit of $2,000 and handles the rest in monthly installments of $300 each, determine the total number of installments required to clear the debt.
Step 1: Calculate the total interest added to the contract lifecycle.
Interest = 15% of $8,000 = 0.15 × 8,000 = 1,200
Step 2: Find the total hire purchase value and the remaining total value of installments.
Total HPV = Cash Price + Interest = 8,000 + 1,200 = 9,200
Total value of installments = HPV − Deposit = 9,200 − 2,000 = 7,200
Step 3: Divide by the monthly billing rate to isolate the number of time periods.
Number of Installments = Total Value of installments Monthly installments
Number of Installments = 7,200 300
= 24
Final Answer: Number of Installments = 24 months
An agricultural producer buys a water pump on credit. The terms demand an initial deposit of $600 and 24 monthly payments of $75 each. If the hire purchase option ends up costing the farmer an extra 25% relative to the immediate buyout option, calculate both the cash price and the Hire Purchase Interest amount.
Step 1: Work out the structural hire purchase payment total.
Total Installments = 24 × 75 = 1,800
HPV = Deposit + Total Installments = 600 + 1,800 = 2,400
Step 2: Construct the algebraic ratio using the extra cost percentage.
Since the hire purchase costs 25% more than the cash price, the Hire Purchase Value is 125% of the Cash Price
1.25 × Cash Price = 2,400
Cash Price = 2,400 ÷ 1.25 = 1,920
Step 3: Subtract the calculated cash price to isolate the absolute interest fee value.
Hire Purchase Interest = HPV − Cash Price
= 2,400 − 1,920
= 480
Final Answer:
Cash Price = $1,920
Hire Purchase Interest = $480
Attempt the following Questions:
(i) A commercial display refrigerator has an outright cash price of $3,500. Under a hire purchase financing scheme, a baker pays a down payment deposit of $800 followed by 24 consecutive monthly installments of $145 each. Calculate the total hire purchase value and determine the flat interest fee charged over the cash price.
(ii) The cash price of a heavy-duty power generator is tagged at $6,400. A workshop acquires it on credit terms by paying an upfront deposit of 15% based on the cash price, with the remaining balance spread over 18 equal monthly installments. If the total hire purchase price ends up being $7,624, calculate the exact amount of each monthly installment.
(iii) A logistics company secures an industrial packaging machine on hire purchase terms by paying a deposit of $1,200 alongside 12 consecutive monthly payments of $450 each. If the interest added by the finance company corresponds to exactly 20% of the machine's original cash price, determine its outright cash price value.
(iv) An agricultural milling machine has an advertised cash price of $12,000. The credit vendor imposes a total finance interest charge equal to 18% of the cash price. If a cooperative pays a standard down payment deposit of $3,160 and agrees to clear the rest of the debt in fixed monthly installments of $550 each, determine the total number of months required to complete the payment contract.
(v) A local wood workshop purchases a specialized CNC router on credit terms requiring an initial deposit of $1,500 and 36 consecutive monthly installments of $175 each. If choosing this hire purchase path ends up costing the workshop an extra 30% compared to buying it immediately upfront, calculate both the original cash price and the absolute value of the interest penalty paid.
HPV = Deposit + Total Value Of Installments
Interest = Hire Purchase Value − Cash Price.
Monthly Installment = Hire Purchase − Deposit Number of months
Hire Purchase Interest Percentage = Interest Cash Price × 100%
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