Step by step
The question
Question: Ellie puts $1200 in a bank at 2% simple interest per year.
How much interest does she earn in 5 years?
1 Find what we know
What do we know?
The money put in: $1200.
The rate: 2% each year.
The time: 5 years.
What do we want?
The interest.
2 Name the unknown
We don't know the interest.
So we call it x.
2% means 2 out of 100: 2/100.
Interest is extra money paid for using money: a bank pays it to you when you save.
The rate is the percent paid each year.
Each year the interest is the rate of the money.
For more years, we multiply by the years.
So here is the rule for interest: money put in, times the rate, times the years.
In short: I = P × r × t.
I is the interest, P the money put in, r the rate, and t the years.
Simple interest is the same amount every year.
3 Write the equation
In words: the money put in, times the rate, times the years, makes the interest.
So the equation is x = 1200 × 2/100 × 5.
Now we solve it.
Careful!
2% is not 2.
It means 2 out of 100: 2/100.
Without the 100, the interest would be $12000: more than the money put in!
4 Multiply the numbers we know
Cancel first.
100 goes into 1200: 100 × 12 = 1200.
So 100 goes into both.
We divide both by 100.
1200 becomes 12, and the 100 is gone.
We write it again, without the crossed-out parts.
Multiply: 12 times 2 times 5 is 120.
Now we have x = 120.
5 Answer the question
So the interest is $120.
6 Check
Let's check in the story.
In 1 year: 2/100 of $1200 is $24.
5 years: $120 of interest, the same as our answer.
Check it with the picture.
Each year: $24.
All the interest: $120.
Does it make sense?
The interest is less than the money put in.
That makes sense for 2% a year.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.