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Ratio & Proportion · Foundation & Higher

Simple interest

Simple interest is calculated on the original principal only. The interest is the same each year and does not compound. It is typically used in savings and loans questions.

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Key facts to remember

  • 1Simple interest formula: I = PRT/100, where P = principal, R = rate per year, T = time in years.
  • 2Total amount = P + I.
  • 3Interest is the same each year — it does not grow over time.
  • 4Simple interest is different from compound interest — it does not reinvest interest.
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Formulas

Simple interest
I = PRT / 100

P = principal, R = annual rate (%), T = time (years)

Total amount
A = P + I
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Worked examples

Example 1

Find the simple interest on £2000 at 3% per year for 4 years.

Working

  1. I = PRT / 100
  2. I = 2000 × 3 × 4 / 100 = 24000 / 100 = £240
Answer£240
Example 2

How many years does it take for £500 to earn £75 simple interest at 5% per year?

Working

  1. 75 = 500 × 5 × T / 100
  2. 75 = 25T
  3. T = 75 ÷ 25 = 3 years
Answer3 years
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Common mistakes

✗Forgetting to divide by 100 in the formula (treating R as a decimal when using I = PRT).
✗Confusing simple interest (same each year) with compound interest (grows each year).
✗Giving the interest as the total amount instead of just the interest earned.
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Exam tips

✓Remember: simple interest = same amount added each year. Total = original + all interest.
✓Rearrange the formula to find P, R or T if required — it's just straightforward algebra.

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