EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
Ratio, Proportion & Rates of Change

Sheet № 177 · Foundation + Higher · AQA · Edexcel · OCR

177

Simple Interest –

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.

§Key definitions

Question:

£500 is invested at 3% simple interest per year. How much interest is earned after 4 years?

Answer:

5% per year

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.

§Formulas to memorise

Simple Interest I = (P × R × T) ÷ 100, where P = principal, R = rate (% per year), T = time (years)

Total amount after T years = P + I = P + (PRT ÷ 100)

Substitute into I = PRT ÷ 100 to find the interest.

I = PRT ÷ 100

I = (500 × 3 × 4) ÷ 100

I = 6000 ÷ 100

I = 60

Interest earned = £1500 − £1200 = £300

R = 300 ÷ 60

R = 5

Worked example

£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

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.
MMXXVI specification · AQA · Edexcel · OCRgcsemathsai.co.uk/formulas/simple-interest