Hire Purchase (HP)

Master the calculations for buying on credit

CAPS Grade 10 Mathematics

In the CAPS curriculum, Hire Purchase (HP) is a fundamental topic that frequently appears in exams. This document provides a comprehensive guide to mastering the calculations involved in HP, focusing on the application of Simple Interest. Each section includes interactive games and quizzes to test your understanding.

Learning Outcomes

  • Calculate deposit as a percentage of cash price
  • Determine the loan amount (principal) after deposit
  • Apply simple interest formula to find total repayment
  • Add insurance fees when applicable
  • Calculate monthly installments
  • Solve real-world Hire Purchase problems

The HP Recipe

Simple Interest Formula
I = P × r × t
A = P + I
where:
P = Principal (loan amount after deposit)
r = Interest rate (as decimal)
t = Time in years
I = Interest amount
A = Total repayment amount
1

Calculate Deposit

Deposit is usually a percentage of the cash price.

Deposit = Cash Price × (percentage/100)
2

Find Loan Amount (P)

Subtract deposit from cash price.

P = Cash Price - Deposit
3

Calculate Total Repayment (A)

Use simple interest formula.

I = P × r × t
A = P + I
4

Add Insurance (If any)

Total = A + (Insurance × months)
5

Calculate Monthly Installments

Monthly = Total ÷ n
n = years × 12

Quiz 1 - HP Steps

What is the first step in a Hire Purchase calculation?

A) Calculate interest
B) Calculate deposit
C) Calculate monthly payment
D) Add insurance

Practice Scenario

Laptop Hire Purchase

Scenario Details
  • Cash Price of Laptop: R12,000
  • Deposit: 10%
  • Interest Rate: 15% per annum
  • Repayment Period: 3 years
Step-by-Step Solution
  1. Step 1: Calculate Deposit
    Deposit = 10% of R12,000 = 0.10 × 12,000 = R1,200
  2. Step 2: Find Loan Amount (P)
    P = R12,000 - R1,200 = R10,800
  3. Step 3: Calculate Interest (I)
    r = 15% = 0.15, t = 3 years
    I = P × r × t = R10,800 × 0.15 × 3 = R4,860
  4. Step 3: Calculate Total Repayment (A)
    A = P + I = R10,800 + R4,860 = R15,660
  5. Step 5: Calculate Monthly Installments
    n = 3 × 12 = 36 months
    Monthly = R15,660 ÷ 36 = R435

Summary of Calculations

Deposit: R1,200
Loan Amount (P): R10,800
Interest (I): R4,860
Total Repayment (A): R15,660
Monthly Payment: R435

Quiz 2 - Laptop HP

What is the loan amount (P) after paying the 10% deposit on R12,000?

A) R1,200
B) R10,800
C) R12,000
D) R15,660

Adding Insurance

HP with Insurance

Scenario

Same laptop but with R25 monthly insurance fee.

Solution
  1. From previous: A = R15,660
  2. Insurance total: R25 × 36 = R900
  3. New total: R15,660 + R900 = R16,560
  4. Monthly payment: R16,560 ÷ 36 = R460

Quiz 3 - Insurance

If monthly insurance is R20 for 24 months, what is total insurance?

A) R240
B) R480
C) R360
D) R400

Practice & Assess

Test your knowledge with these interactive games.

Match - Steps to Descriptions

Step 1
Calculate deposit
Step 2
Find loan amount
Step 3
Calculate interest
Step 5
Monthly installments

Fill - Simple Interest

I = P × ___ × t

Practice Questions

Q1

Cash price R8,000, deposit 15%, interest 12% p.a., 2 years. Find monthly payment.

Q2

TV costs R15,000, deposit 20%, interest 10% p.a., 3 years. Calculate total repayment.

Q3

Fridge R5,000, deposit 10%, interest 18% p.a., 2 years with R15 monthly insurance. Find monthly payment.

Answers

Q1: R308.89 | Q2: R16,800 | Q3: R216.67

Common Errors to Avoid

Error 1

Interest on full price: Forgetting to subtract deposit first

Solution: Always calculate P = Cash Price - Deposit

Error 2

Wrong months: Forgetting to convert years to months

Solution: n = years × 12

Error 3

Decimal conversion: Using 15 instead of 0.15 for 15%

Summary of Key Concepts

Deposit: % of cash price
Loan Amount (P): Cash Price - Deposit
Simple Interest: I = P × r × t
Total Repayment: A = P + I
Monthly Payment: (A + Insurance) ÷ (years × 12)

Key Terms

Hire Purchase Deposit Principal Loan Amount Simple Interest Interest Rate Insurance Monthly Installment Total Repayment Cash Price
Compound Interest Inflation