Simple & Compound Interest, Growth & Decay

Revise Simple & Compound Interest, Growth & Decay for Mathematics 0580 (O Level) — revision notes and instant AI marking.

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Simple Interest

Interest calculated on the original amount only—always the same each period

What is Simple Interest?

Interest is money that's regularly added to an original amount. When you save money in a bank, the bank pays you interest. When you borrow money, you pay interest.

Simple interest is the easiest type of interest to calculate. It's based only on the original (starting) amount. Each year (or time period), you earn or pay the same amount of interest.

Why "simple"? Because the interest calculation never changes. If you earn $10 interest in year 1, you'll earn $10 in year 2, year 3, and every year after. The interest doesn't "build on itself" like compound interest does.

Think of it like a vending machine that pays you exactly the same amount every day, no matter what. In compound interest, the payment would increase each day.

How do I Calculate Simple Interest?

There are two things you might need to find:

1. The interest earned (or owed) — how much money is added/paid

2. The total balance — the original amount plus interest

Simple Interest Calculation:

Step 1: Find the percentage of the starting amount
(Use a multiplier: 0.04 for 4%, 0.05 for 5%, etc.)

Step 2: Multiply by the number of time periods (usually years)

Step 3: For total balance, add this to the starting amount

Example: $250 saved at 4% simple interest for 6 years. Find total interest earned.

Step 1: Find 4% of $250: 0.04 × 250 = $10

Step 2: This is earned each year for 6 years: $10 × 6 = $60

Answer: $60 interest earned

Total balance: $250 + $60 = $310

Key Point: With simple interest, the amount earned each period is always the same. Year 1: $10. Year 2: $10. Year 3: $10. This makes it "simple" but also less rewarding than compound interest.

❌ Common Mistake: Multiplying only once. Some students do 250 × 1.04 = 260, forgetting that this happens every year. You must multiply by the percentage AND by the number of years: 250 × 0.04 × 6 = $60.

Finding the Interest Rate (Reverse Problem)

Sometimes you're told the final amount and need to find the rate. The method is to work backwards:

Finding the Rate:

Step 1: Find the total interest (final amount − original amount)
Step 2: Divide by the number of years (interest per year)
Step 3: Divide by original amount and convert to percentage

Example: £9000 invested at n% simple interest per year. After 5 years: £11,700. Find n.

Step 1: Total interest: £11,700 − £9000 = £2700

Step 2: Interest per year: £2700 ÷ 5 = £540

Step 3: £540 ÷ £9000 = 0.06 = 6%

Answer: n = 6%

Exam Tip:

Compound Interest

What is Compound Interest?

Compound interest

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Also in the full note

Depreciation
Exponential Growth & Decay
Summary: The Big Picture
Concepts Checklist & Exam Preparation
How do I Calculate Compound Interest?
What if There Are Different Rates?
Reverse Compound Interest (Finding Original Amount)
What is Depreciation?

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