IGCSE Earnings, Simple and Compound Interest: Complete Guide for Cambridge IGCSE Mathematics

IGCSE earnings, simple interest and compound interest are practical topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering salary calculations, simple interest formulas, and compound interest formulas is essential for solving real-world financial problems and achieving top grades.

This comprehensive IGCSE earnings, simple and compound interest guide covers everything you need to know, including calculating wages and salaries, commission and overtime pay, simple interest calculations, compound interest with different compounding periods, step-by-step worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to calculate earnings from different payment structures, solve simple and compound interest problems, and apply these skills to real-world financial scenarios in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Financial Mathematics practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Earnings, Simple and Compound Interest Matter

IGCSE earnings, simple interest and compound interest are practical topics with real-world applications. Here’s why they’re so important:

• High frequency topic: Financial mathematics questions appear regularly in IGCSE maths papers
• Real-world applications: Essential for understanding personal finance, banking, and investments
• Exam weight: Typically worth 6-10 marks per paper
• Practical skills: Develops financial literacy and problem-solving abilities
• Foundation for advanced topics: Essential for understanding exponential growth and financial modeling

Key insight from examiners: Students often confuse simple and compound interest, or make errors in calculating earnings with multiple components. This guide will help you master these systematically.

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Understanding Earnings: The Basics

Earnings refer to the money a person receives for work. Different payment structures include:

• Salary: Fixed annual amount, usually paid monthly
• Wage: Payment per hour worked
• Commission: Percentage of sales
• Overtime: Extra payment for hours worked beyond normal hours
• Bonus: Additional payment for performance

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Calculating Earnings

Basic Wage Calculation

Formula: Total Wage = Hourly Rate × Hours Worked

Example: If someone earns $15 per hour and works 40 hours, find their total wage.

Solution: Total Wage = $15 × 40 = $600

Answer: $600

Salary Calculation

Monthly salary from annual: Monthly Salary = Annual Salary ÷ 12

Example: An annual salary is $48,000. Find the monthly salary.

Solution: Monthly Salary = $48,000 ÷ 12 = $4,000

Answer: $4,000 per month

Commission

Formula: Commission = Commission Rate × Sales Amount

Example: A salesperson earns 5% commission on sales. If they make $8,000 in sales, find their commission.

Solution: Commission = 5% × $8,000 = 0.05 × $8,000 = $400

Answer: $400

Overtime Pay

Overtime is usually paid at a higher rate (e.g., 1.5× or 2× the normal rate).

Formula: Overtime Pay = Overtime Rate × Overtime Hours

Example: Normal rate is $20/hour. Overtime is paid at 1.5× the normal rate. If someone works 5 hours overtime, find their overtime pay.

Solution:

1. Overtime rate: 1.5 × $20 = $30/hour
2. Overtime pay: $30 × 5 = $150

Answer: $150

Total Earnings with Multiple Components

Example: A worker earns:

• Base wage: $18/hour for 35 hours
• Overtime: $27/hour (1.5×) for 5 hours
• Commission: 3% on $5,000 sales

Find total earnings.

Solution:

1. Base wage: $18 × 35 = $630
2. Overtime: $27 × 5 = $135
3. Commission: 3% × $5,000 = $150
4. Total: $630 + $135 + $150 = $915

Answer: $915

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Understanding Simple Interest

Simple interest is interest calculated only on the principal (original amount), not on previously earned interest.

Simple Interest Formula

Formula: I = PRT

Where:

• I = Interest
• P = Principal (initial amount)
• R = Rate (as a decimal, e.g., 5% = 0.05)
• T = Time (in years)

Total Amount Formula: A = P + I = P(1 + RT)

Key Points

• Interest is calculated only on the principal
• The interest amount is the same each year
• Time must be in years (convert months to years: months ÷ 12)

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Worked Examples: Simple Interest

Example 1: Basic Simple Interest

Calculate the simple interest on $5,000 at 4% per annum for 3 years.

Solution: I = PRT = $5,000 × 0.04 × 3 = $600

Answer: $600

Example 2: Total Amount

Find the total amount after investing $8,000 at 6% simple interest for 5 years.

Solution:

1. Interest: I = $8,000 × 0.06 × 5 = $2,400
2. Total amount: A = $8,000 + $2,400 = $10,400

Alternative: A = P(1 + RT) = $8,000(1 + 0.06 × 5) = $8,000 × 1.30 = $10,400

Answer: $10,400

Example 3: Time in Months

Calculate simple interest on $3,000 at 5% per annum for 18 months.

Solution:

1. Convert months to years: 18 months = 18/12 = 1.5 years
2. Interest: I = $3,000 × 0.05 × 1.5 = $225

Answer: $225

Example 4: Finding the Rate

$2,000 invested at simple interest becomes $2,300 after 2 years. Find the interest rate.

Solution:

1. Interest earned: $2,300 - $2,000 = $300
2. Using I = PRT: $300 = $2,000 × R × 2
3. $300 = $4,000R
4. R = $300/$4,000 = 0.075 = 7.5%

Answer: 7.5%

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Understanding Compound Interest

Compound interest is interest calculated on both the principal and previously earned interest. This means the interest grows exponentially.

Compound Interest Formula

Formula: A = P(1 + r/n)^(nt)

Where:

• A = Final amount
• P = Principal (initial amount)
• r = Annual interest rate (as a decimal)
• n = Number of times interest is compounded per year
• t = Time (in years)

Interest Earned: I = A - P

Common Compounding Periods

• Annually: n = 1 (once per year)
• Semi-annually: n = 2 (twice per year)
• Quarterly: n = 4 (four times per year)
• Monthly: n = 12 (twelve times per year)
• Daily: n = 365 (365 times per year)

Simplified Formula (Annual Compounding)

If compounded annually: A = P(1 + r)^t

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Worked Examples: Compound Interest

Example 1: Annual Compounding

Calculate the compound interest on $10,000 at 5% per annum, compounded annually, for 3 years.

Solution:

1. A = P(1 + r)^t = $10,000(1 + 0.05)³
2. A = $10,000 × 1.05³ = $10,000 × 1.157625 = $11,576.25
3. Interest: I = $11,576.25 - $10,000 = $1,576.25

Answer: $1,576.25

Example 2: Quarterly Compounding

Calculate the amount after investing $5,000 at 6% per annum, compounded quarterly, for 2 years.

Solution:

1. r = 0.06, n = 4, t = 2
2. A = P(1 + r/n)^(nt) = $5,000(1 + 0.06/4)^(4×2)
3. A = $5,000(1.015)^8
4. A = $5,000 × 1.12649 = $5,632.45

Answer: $5,632.45

Example 3: Monthly Compounding

$8,000 is invested at 4% per annum, compounded monthly, for 18 months. Find the final amount.

Solution:

1. r = 0.04, n = 12, t = 18/12 = 1.5 years
2. A = $8,000(1 + 0.04/12)^(12×1.5)
3. A = $8,000(1.00333...)^18
4. A = $8,000 × 1.06168 = $8,493.44

Answer: $8,493.44

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Comparing Simple and Compound Interest

Key difference:

• Simple interest: Linear growth (same amount each year)
• Compound interest: Exponential growth (increases each year)

Example: Compare $1,000 at 10% for 3 years:

Simple Interest:

• Year 1: $1,000 + $100 = $1,100
• Year 2: $1,100 + $100 = $1,200
• Year 3: $1,200 + $100 = $1,300

Compound Interest (annually):

• Year 1: $1,000 × 1.10 = $1,100
• Year 2: $1,100 × 1.10 = $1,210
• Year 3: $1,210 × 1.10 = $1,331

Compound interest gives more because interest earns interest!

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Step-by-Step Method for Interest Problems

1. Identify the type - Simple or compound interest?
2. List the given information - P, R, T (and n for compound)
3. Convert units - Ensure time is in years, rate is decimal
4. Apply the formula - Use the correct formula
5. Calculate carefully - Use calculator efficiently
6. Check your answer - Does it make sense?

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Common Examiner Traps (and How to Dodge Them)

• Confusing simple and compound interest - Simple: same interest each year. Compound: interest on interest
• Time unit errors - Always convert months to years (divide by 12)
• Rate conversion - Always convert percentage to decimal (divide by 100)
• Compounding frequency - Pay attention to “compounded annually/quarterly/monthly”
• Forgetting to subtract principal - Interest = Final Amount - Principal
• Order of operations - Use brackets correctly in compound interest formula

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IGCSE Earnings, Simple and Compound Interest Practice Questions

Question 1: Earnings

A worker earns $22/hour for 38 hours, plus 1.5× for 4 hours overtime, and 2% commission on $6,000 sales. Find total earnings.

Solution:

1. Base: $22 × 38 = $836
2. Overtime: 1.5 × $22 × 4 = $132
3. Commission: 2% × $6,000 = $120
4. Total: $836 + $132 + $120 = $1,088

Answer: $1,088

Question 2: Simple Interest

Calculate simple interest on $12,000 at 3.5% per annum for 2.5 years.

Solution: I = $12,000 × 0.035 × 2.5 = $1,050

Answer: $1,050

Question 3: Compound Interest

$15,000 is invested at 5% per annum, compounded annually, for 4 years. Find the final amount.

Solution: A = $15,000(1.05)⁴ = $15,000 × 1.21551 = $18,232.65

Answer: $18,232.65

Question 4: Quarterly Compounding

$7,500 is invested at 6% per annum, compounded quarterly, for 3 years. Find the interest earned.

Solution:

1. A = $7,500(1 + 0.06/4)^(4×3) = $7,500(1.015)^12
2. A = $7,500 × 1.19562 = $8,967.15
3. Interest: $8,967.15 - $7,500 = $1,467.15

Answer: $1,467.15

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Frequently Asked Questions About IGCSE Earnings, Simple and Compound Interest

What’s the difference between simple and compound interest?

• Simple interest: Calculated only on the principal (same amount each year)
• Compound interest: Calculated on principal + previously earned interest (grows each year)

How do I calculate simple interest?

Use I = PRT where P = principal, R = rate (as decimal), T = time (in years).

How do I calculate compound interest?

Use A = P(1 + r/n)^(nt) where n = compounding frequency per year.

What does “compounded quarterly” mean?

Interest is calculated and added 4 times per year (every 3 months).

How do I convert months to years?

Divide by 12. Example: 18 months = 18/12 = 1.5 years.

How do I calculate total earnings with multiple components?

Add all components: base wage + overtime + commission + bonus, etc.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Fractions, Decimals and Percentages: Complete Guide - Master conversions and calculations
• IGCSE Exponential Growth and Decay: Complete Guide - Master exponential functions
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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