Percentages (I) · Ages 12–13
Simple and compound interest
Simple: principal × rate × years; compound: multiply year by year.
How to do it
Method
Simple: principal × rate × years; compound: multiply year by year
5000 × 3% × 4 = 600, amount 5600
Another way
A year's interest first
5000 × 3% = 150, 150 × 4 = 600
In full
Money saved or borrowed, the principal, earns interest at a yearly rate. Simple interest is on the principal alone: interest = principal × rate × years, and the amount = principal + interest. $5000 at 3% a year for 4 years: one way, a year's interest first, 5000 × 3% = 150, then times 4 years, 600. Another, the formula: 5000 × 3% × 4 = 600. The amount is 5600. Months become years: 6 months is 0.5 years. To find the principal, the rate or the time from the interest, turn the formula round and divide. Compound interest adds each year's interest to the principal before the next: amount = principal × (1 + rate)^years. $1000 at 10% for two years grows to 1000 × 1.1 × 1.1 = 1210, $10 more than simple interest. When the question asks for the interest, take the principal off.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Principal $16,500 at 1.5% a year for 8 years: simple interest = $
Show the answer and working
Answer: 1,980
Interest = principal × rate × years = 16500 × 1.5% × 8 = 1980.
Example 2
A principal of $20,000 at 6% a year for 3 years: what is the simple interest?
- A. $3,600
- B. $23,600
- C. $1,200
- D. $3,820.32
Choose the right answer
Show the answer and working
Answer: A. $3,600
20000 × 6% × 3 = 3600. Or one year's interest, 1200, times 3.
Example 3
A principal of $8,000 at 6% a year earned $960 in simple interest. For how many years?
Show the answer and working
Answer: 2 years
A year's interest is 8000 × 6% = 480, and 960 ÷ 480 = 2 years.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.On $5,000 at 3% a year, the simple interest for 5 years is $750.
True or false?
Answer:
2.Principal $5,000 at 5.5% a year for 5 years: one year's interest = $, the simple interest for 5 years = $, the amount = $.
Fill in each blank
Answer:
3.Principal $10,000 for 4 years earns $2,800 simple interest: the yearly rate = %
Answer:
4.Principal $14,600 at 1% a year for 30 months: simple interest = $
Answer:
5.Principal $9,000 at 6% a year, compounded yearly. The amount after 2 years = $
Answer:
All the answers
- 1. True
- 2. 275, 1,375, 6,375
- 3. 7
- 4. 365
- 5. 10,112.4
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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