Step by step
The question
Question: Sam borrows $2400 at 5% simple interest per year.
How much will he owe after 6 months?
1 Find what we know
What do we know?
The money put in: $2400.
The rate: 5% each year.
The time: 6 months.
What do we want?
All the money at the end.
2 Name the unknown
We don't know the interest.
So we call it x.
5% means 5 out of 100: 5/100.
A year has 12 months.
So 6 months is 6/12, 1/2 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 = 2400 × 5/100 × 1/2.
Now we solve it.
4 Multiply the numbers we know
Cancel first.
2400 and 100 can both be divided by 100.
2400 becomes 24, and the 100 is gone.
Write what is left.
Multiply the whole numbers: 120.
So x is 120/2.
120 divided by 2 is 60.
So x = 60!
5 Answer the question
All the money: the $2400 put in, plus $60 interest, is $2460.
Careful!
The interest alone is not the answer.
The question asks for all the money: the money put in, plus the interest.
So there is $2460 at the end.
6 Check
Let's check in the story.
In 1 year: 5/100 of $2400 is $120.
1/2 of a year: $60 of interest.
Plus the money put in: $2460.
Does it make sense?
The interest is less than the money put in.
That makes sense for 5% 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.