Simple interest is a straightforward way of calculating the interest earned or charged on a sum of money. Unlike compound interest, the interest is calculated only on the original amount and stays the same each year.
What Is Simple Interest?
Simple interest is interest that is calculated on the original principal (starting amount) only. The same fixed amount of interest is added each year, regardless of any interest already earned. This makes it easy to calculate with a single formula.
In contrast, compound interest calculates interest on the principal plus any previously earned interest, so the amount grows faster over time. GCSE questions often ask you to compare the two methods.
Simple interest is commonly used for short-term loans, hire-purchase agreements, and savings accounts with fixed annual payouts.
Because the interest is the same each year, a simple interest investment grows in a straight line when plotted on a graph, unlike compound interest which curves upwards.
Key Formulas
Step-by-Step Method
- Identify P (the starting amount), R (the annual interest rate as a percentage), and T (the number of years).
- Substitute into I = PRT ÷ 100 to find the interest.
- Add the interest to the principal if the question asks for the total amount.
Worked Example 1 — Foundation Level
Question: £500 is invested at 3% simple interest per year. How much interest is earned after 4 years?
Working: I = PRT ÷ 100 I = (500 × 3 × 4) ÷ 100 I = 6000 ÷ 100 I = 60
Answer: £60
Worked Example 2 — Higher Level
Question: £1200 is invested at simple interest. After 5 years the total amount is £1500. Find the annual interest rate.
Working: Interest earned = £1500 − £1200 = £300 I = PRT ÷ 100 300 = (1200 × R × 5) ÷ 100 300 = 6000R ÷ 100 300 = 60R R = 300 ÷ 60 R = 5
Answer: 5% per year
Worked Example 3 — Exam Style
Question: Ali invests £800 at 4% simple interest. Ben invests £800 at 3.5% compound interest. Who has more money after 3 years?
Working: Ali (simple): I = (800 × 4 × 3) ÷ 100 = 96. Total = £896. Ben (compound): Year 1: 800 × 1.035 = £828. Year 2: 828 × 1.035 = £856.98. Year 3: 856.98 × 1.035 = £886.97 (2 d.p.) Ali: £896 vs Ben: £886.97
Answer: Ali has more money after 3 years (£896 vs £886.97).
Common Mistakes
- Using compound interest instead of simple interest. With simple interest, the same amount is added each year. If you multiply the running total by a multiplier each year, you are calculating compound interest.
- Forgetting to divide by 100. The rate R is a percentage. If you forget to divide by 100, your answer will be 100 times too large.
- Not adding interest to the principal. I = PRT/100 gives the interest only. If the question asks for the total amount, you must add the interest to the original principal.
- Using months instead of years. T must be in years. For 6 months, use T = 0.5.
Exam Tips
- Simple interest produces a linear growth — the same amount each year. If a question mentions "the same amount of interest each year," it is simple interest.
- Compound interest produces exponential growth. Questions asking you to compare the two are common.
- Always state whether your final answer is the interest or the total amount, depending on what the question asks.
Practice Questions
Q1 (Foundation): £2000 is invested at 2.5% simple interest per year for 6 years. Find the total interest earned.
Q2 (Foundation): £350 is saved at 4% simple interest. What is the total amount after 3 years?
Q3 (Higher): An investment of £P earns £180 in simple interest over 6 years at 5% per year. Find P.
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Related Topics
Summary
- Simple interest is calculated on the original principal only: I = PRT ÷ 100.
- The same amount of interest is earned each year.
- Total amount = principal + interest.
- Simple interest grows linearly, while compound interest grows exponentially.
- Always check whether the question asks for the interest or the total amount.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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