Step by step
The question
Question: Tom wants to earn $200 interest in 4 years.
The bank pays 5% simple interest per year.
How much must he put in?
1 Find what we know
What do we know?
The interest: $200.
The time: 4 years.
The rate: 5% each year.
What do we want?
The money put in.
2 Name the unknown
We don't know the money put in.
So we call it x.
5% means 5 out of 100: 5/100.
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 × 5/100 × 4 = 200.
Now we solve it.
Careful!
5% is 5 out of 100.
So in the rule it is 5/100, not 5.
4 Multiply the numbers we know
The numbers we know: 5/100, times 4 years.
5 times 4 is 20.
So x times 20/100.
Simplify: 20/100 is 1/5.
x times 1/5 is x/5.
5 Remove the fraction
The bottom number is 5.
Times 5 will remove it.
We multiply every part by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
Write what is left.
Do the multiplications.
No more fractions!
So x = 1000!
6 Answer the question
So the money put in is $1000.
7 Check
Let's check in the story.
In 1 year: 5/100 of $1000 is $50.
4 years: $200 of interest, like the story says.
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.