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