Step by step
The question
Question: Dan borrows $1500 at 8% simple interest per year.
How much interest does he pay in 9 months?
1 Find what we know
What do we know?
The money put in: $1500.
The rate: 8% each year.
The time: 9 months.
What do we want?
The interest.
2 Name the unknown
We don't know the interest.
So we call it x.
8% means 8 out of 100: 8/100.
A year has 12 months.
So 9 months is 9/12, 3/4 of a year.
Here is the rule for it.
Interest = money put in, times the rate, times the years.
In short: I = P × r × t.
Interest is extra money for using money.
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 = 1500 × 8/100 × 3/4.
Now we solve it.
Careful!
8% is not 8.
It means 8 out of 100: 8/100.
Without the 100, the interest would be $9000: more than the money put in!
4 Multiply the numbers we know
Cancel first.
1500 and 100 can both be divided by 100.
1500 becomes 15, and the 100 is gone.
Write what is left.
Multiply the whole numbers: 120.
Times the top 3: 360.
So x is 360/4.
360 divided by 4 is 90.
So x = 90!
5 Answer the question
So the interest is $90.
6 Check
Let's check in the story.
In 1 year: 8/100 of $1500 is $120.
3/4 of a year: $90 of interest, like the story says.
Does it make sense?
The interest is less than the money put in.
That makes sense for 8% 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.