Percentages · Usually met around P6
Simple interest
Interest = money × yearly rate × years.
How to do it
Method
Interest = money × yearly rate × years
$5000 at 3% for 4 years: 5000 × 3100 × 4 = 600
Another way
Add the interest year by year
5000 → 5150 → 5300 → 5450 → 5600
In full
Money kept in a bank earns interest. Simple interest is worked out on the money first put in, every year, so each year's interest is the same: interest = money put in × yearly rate × number of years. $5000 for 4 years at 3% a year: each year 5000 × 3100 = $150, so 4 years give 150 × 4 = $600, and the money with interest is 5000 + 600 = $5600. Another way: make a table and add $150 a year: 5000, 5150, 5300, 5450, 5600. It works backwards too: interest ÷ one year's interest = the years; one year's interest ÷ the money × 100 = the rate. Borrowing works the same way, except the borrower pays the interest.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
$1000 is put in a bank at 1% a year, simple interest. How much is there after 2 years, money and interest together?
Show the answer and working
Answer: 1020 dollars
Interest for 2 years: 1000 × 1100 × 2 = 20; 1000 + 20 = 1020.
Example 2
Some money is put in a bank with simple interest: after 1 year there is $9360, after 2 years $9720 and after 3 years $10080, money and interest together. Going on like this, how much is there after 10 years?
Show the answer and working
Answer: 12600 dollars
Each year adds 9720 − 9360 = 360; the money put in was 9360 − 360 = 9000; after 10 years: 9000 + 360 × 10 = 12600.
Example 3
$8000 is put in a bank at 5% a year, simple interest. After 5 years there is $10000 in all, money and interest together.
True or false?
Show the answer and working
Answer: True
Interest is 400 a year, 2000 in 5 years; with the money, 8000 + 2000 = 10000.
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