🏠 Home › 📚 CSEC Mathematics › 💰 Hire Purchase and Mortgages

Mastering Hire Purchase and Mortgages

CSEC Mathematics: Real-World Financial Mathematics

Essential Understanding: Hire Purchase (HP) and Mortgages are practical applications of percentage, interest, and installment calculations. These financial arrangements allow people to acquire expensive items or properties by paying over time with interest. Master these concepts to make informed financial decisions and excel in consumer arithmetic questions.

🔑 Key Skill: Calculating Monthly Payments

📈 Exam Focus: Hire Purchase vs Cash Price

🎯 Problem Solving: Mortgage Interest Calculations

Core Concepts

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Hire Purchase (HP)

Definition: A method of buying goods where the buyer pays a deposit and makes regular installment payments (usually monthly) until the full price plus interest is paid.

Key Terms:

Cash Price: The price if paid in full immediately
Deposit: Initial payment (usually a percentage)
Balance: Cash price minus deposit
Interest: Extra charge for borrowing

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Mortgage

Definition: A loan specifically for purchasing property, where the property itself serves as collateral. The borrower repays the loan with interest over a long period (15-30 years).

Key Terms:

Principal: The amount borrowed
Interest Rate: Annual percentage charged
Term: Loan repayment period
Amortization: Gradual repayment through installments

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Deposit

Definition: An initial payment made when entering a hire purchase agreement or mortgage.

Calculation: Usually expressed as a percentage of the cash price.

\[ \text{Deposit} = \text{Cash Price} \times \frac{\text{Deposit Percentage}}{100} \]

Example: 10% deposit on $5,000 = $500

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Interest on HP

Definition: The extra amount paid for the privilege of paying in installments.

Calculation:

\[ \text{Total Interest} = \text{Total HP Price} – \text{Cash Price} \]

\[ \text{Monthly Interest} = \frac{\text{Total Interest}}{\text{Number of Months}} \]

Interest rates are usually given as simple interest per annum.

Key Formulas

Hire Purchase Total Price

\[ \text{Total HP Price} = \text{Deposit} + (\text{Monthly Payment} \times \text{n}) \]

Balance to be Financed

\[ \text{Balance} = \text{Cash Price} – \text{Deposit} \]

Monthly Payment

\[ \text{Monthly Payment} = \frac{\text{Balance} + \text{Interest}}{\text{Number of Months}} \]

Hire Purchase vs Mortgage Comparison

Aspect	Hire Purchase	Mortgage
Purpose	Buying consumer goods (cars, appliances)	Buying real estate (houses, land)
Duration	Short to medium term (1-5 years)	Long term (15-30 years)
Interest Rate	Usually higher (simple interest)	Usually lower (compound interest)
Deposit	Typically 10-30% of cash price	Typically 10-20% of property value
Ownership	Ownership transfers after final payment	Property serves as collateral; ownership with deed
CSEC Focus	Simple interest calculations	Compound interest calculations

Interactive Payment Calculator

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Compare Payment Options

Objective: Adjust the parameters to see how different deposit amounts, interest rates, and loan terms affect monthly payments and total costs.

Calculation Type

Cash Price/Principal ($)

Deposit (%)

Interest Rate (% per annum)

Term (years)

Monthly Payment

$0.00

Total Interest

$0.00

Total Cost

$0.00

Calculation Details

Adjust the values and click “Calculate Payments” to see detailed results.

Worked Examples

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Example 1: Hire Purchase Car Purchase

Problem: A car has a cash price of $24,000. It can be bought on hire purchase by paying a 25% deposit and 24 monthly installments of $850. Calculate:

(a) The deposit amount

(b) The total hire purchase price

Calculate deposit: \[ \text{Deposit} = 25\% \text{ of } \$24,000 = 0.25 \times 24,000 = \$6,000 \]

Calculate total installment payments: \[ \text{Total installments} = 24 \times \$850 = \$20,400 \]

Calculate total HP price: \[ \text{Total HP Price} = \text{Deposit} + \text{Total installments} \] \[ = \$6,000 + \$20,400 = \$26,400 \]

Calculate interest charged: \[ \text{Interest} = \text{Total HP Price} – \text{Cash Price} \] \[ = \$26,400 – \$24,000 = \$2,400 \]

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Example 2: Mortgage Calculation

Problem: A house is valued at $300,000. A buyer pays a 20% deposit and takes a mortgage for the balance at 6% per annum compound interest for 20 years. Calculate the monthly payment (assuming interest is compounded monthly).

Calculate deposit: \[ \text{Deposit} = 20\% \text{ of } \$300,000 = 0.20 \times 300,000 = \$60,000 \]

Calculate mortgage principal: \[ \text{Principal} = \$300,000 – \$60,000 = \$240,000 \]

Use mortgage formula: For CSEC, we often use: \[ \text{Monthly Payment} = \frac{P \times r \times (1+r)^n}{(1+r)^n – 1} \] Where: $P = \$240,000$, $r = \frac{6\%}{12} = 0.005$, $n = 20 \times 12 = 240$

Calculate: \[ \text{Monthly Payment} = \frac{240,000 \times 0.005 \times (1.005)^{240}}{(1.005)^{240} – 1} \] \[ \approx \frac{240,000 \times 0.005 \times 3.310}{3.310 – 1} \] \[ \approx \frac{240,000 \times 0.01655}{2.310} \approx \frac{3,972}{2.310} \approx \$1,719.48 \]

CSEC Past Paper Questions

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CSEC 2018, Paper 2 Question 5(b)

Question: A refrigerator has a cash price of $4,500. It can also be purchased on hire purchase by making a deposit of 15% of the cash price and 24 monthly payments of $180.

(i) Calculate the hire purchase price of the refrigerator.

(ii) Calculate the amount saved by buying the refrigerator for cash instead of on hire purchase.

Calculate deposit: \[ \text{Deposit} = 15\% \text{ of } \$4,500 = 0.15 \times 4,500 = \$675 \]

Calculate total monthly payments: \[ \text{Total monthly} = 24 \times \$180 = \$4,320 \]

Calculate hire purchase price: \[ \text{HP Price} = \text{Deposit} + \text{Total monthly} \] \[ = \$675 + \$4,320 = \$4,995 \]

Calculate amount saved by cash: \[ \text{Savings} = \text{HP Price} – \text{Cash Price} \] \[ = \$4,995 – \$4,500 = \$495 \] So you save $495 by paying cash.

Key Examination Insights

Common Mistakes

Forgetting to subtract the deposit from the cash price before calculating interest.
Confusing simple interest (HP) with compound interest (mortgages).
Calculating interest on the full cash price instead of the balance.
Using years instead of months (or vice versa) in calculations.

Success Strategies

Always write down what each number represents (cash price, deposit, balance, etc.).
Draw a timeline showing deposit, monthly payments, and total period.
For HP problems, calculate the total HP price first, then subtract cash price to find interest.
Check your answer: Total HP price should be greater than cash price.

CSEC Practice Arena

Test Your Understanding

A television set has a cash price of $2,500. It can be bought on hire purchase by paying a 20% deposit and 12 monthly installments of $190. What is the total hire purchase price?

$2,280

$2,780

$2,500

$2,980

Explanation: Deposit = 20% of $2,500 = $500. Total installments = 12 × $190 = $2,280. Total HP price = $500 + $2,280 = $2,780.

A laptop costs $1,800 cash. On hire purchase, a 15% deposit is required plus 18 monthly payments of $95. How much interest is charged on the hire purchase?

$135

$270

$315

$450

Solution: Deposit = 15% of $1,800 = $270. Total installments = 18 × $95 = $1,710. Total HP price = $270 + $1,710 = $1,980. Interest = $1,980 – $1,800 = $180.

A house valued at $200,000 requires a 25% deposit. The balance is financed by a mortgage at 5% per annum simple interest for 15 years. What is the monthly repayment?

$833.33

$937.50

$1,041.67

$1,250.00

Solution: Deposit = 25% of $200,000 = $50,000. Balance = $150,000. Simple interest for 15 years = $150,000 × 0.05 × 15 = $112,500. Total to repay = $150,000 + $112,500 = $262,500. Monthly = $262,500 ÷ (15×12) = $262,500 ÷ 180 = $1,458.33.

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CSEC Examination Mastery Tip

Hire Purchase Strategy: In HP questions, always follow this systematic approach:

Calculate the deposit: Cash price × deposit percentage
Calculate the balance: Cash price – deposit
Calculate total installment payments: Monthly payment × number of months
Calculate total HP price: Deposit + total installments
Calculate interest: Total HP price – cash price

Label each calculation clearly to avoid confusion and ensure you earn method marks even if your final answer is incorrect.